Maths-

General

Easy

Question

# Use the square of a binomial to find the value. 72^{2}

Hint:

### The methods used to find the product of binomials are called special products.

Multiplying a number by itself is often called squaring.

For example (*x* + 3)(*x* + 3) = (*x* + 3)2

## The correct answer is: 5184.

### 72^{2} can be written as (70 + 2)^{2} which can be further written as (70 + 2)(70 + 2)

(70 + 2)(70 + 2) = 70(70 + 2) + 2(70 + 2)

= 70(70) + 70(2) + 2(70) + 2(2)

= 4900 + 140 + 140 + 4

= 4900 + 280 + 4

= 5184

Final Answer:

Hence, the value of 72^{2} is 5184.

Final Answer:

Hence, the value of 72

^{2}is 5184.

### Related Questions to study

Maths-

### What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:

Hint:

The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.

Step by step solution:

The given equation of the line is

-2x + y = -7

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation -2x + y - 7, as below

y = 2x - 7

Comparing with y = mx + c, we get that m = 2

Thus, the gradient of line -2x + y = 7 is m = 2.

We know that the gradient of any two parallel lines in the xy plane is always equal.

Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get

The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.

Step by step solution:

The given equation of the line is

-2x + y = -7

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation -2x + y - 7, as below

y = 2x - 7

Comparing with y = mx + c, we get that m = 2

Thus, the gradient of line -2x + y = 7 is m = 2.

We know that the gradient of any two parallel lines in the xy plane is always equal.

Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get

### What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:

Maths-General

Hint:

The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.

Step by step solution:

The given equation of the line is

-2x + y = -7

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation -2x + y - 7, as below

y = 2x - 7

Comparing with y = mx + c, we get that m = 2

Thus, the gradient of line -2x + y = 7 is m = 2.

We know that the gradient of any two parallel lines in the xy plane is always equal.

Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get

The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.

Step by step solution:

The given equation of the line is

-2x + y = -7

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation -2x + y - 7, as below

y = 2x - 7

Comparing with y = mx + c, we get that m = 2

Thus, the gradient of line -2x + y = 7 is m = 2.

We know that the gradient of any two parallel lines in the xy plane is always equal.

Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get

Maths-

### Two sides of a rectangle are (3p+5q) units and ( 5p-7q ) units. What is its area?

Answer:

The area of the rectangle is the product of sides.

Two sides of a rectangle

(3p+5q) units and ( 5p-7q ) units.

○ Step 1:

We know, the area of rectangle is product of its sides

i.e. area = side × side

So,

Area = (3p+5q) × (5p-7q)

= 3p (5p -7q) + 5q(5p-7q)

= 15p

= 15p

- Hint:

The area of the rectangle is the product of sides.

- Step by step explanation:

Two sides of a rectangle

(3p+5q) units and ( 5p-7q ) units.

○ Step 1:

We know, the area of rectangle is product of its sides

i.e. area = side × side

So,

Area = (3p+5q) × (5p-7q)

= 3p (5p -7q) + 5q(5p-7q)

= 15p

^{2}- 21pq + 25pq - 35q^{2}= 15p

^{2}+ 4pq - 35q^{2}sq. units- Final Answer:

^{2}+ 4pq - 35q^{2}sq. units.### Two sides of a rectangle are (3p+5q) units and ( 5p-7q ) units. What is its area?

Maths-General

Answer:

The area of the rectangle is the product of sides.

Two sides of a rectangle

(3p+5q) units and ( 5p-7q ) units.

○ Step 1:

We know, the area of rectangle is product of its sides

i.e. area = side × side

So,

Area = (3p+5q) × (5p-7q)

= 3p (5p -7q) + 5q(5p-7q)

= 15p

= 15p

- Hint:

The area of the rectangle is the product of sides.

- Step by step explanation:

Two sides of a rectangle

(3p+5q) units and ( 5p-7q ) units.

○ Step 1:

We know, the area of rectangle is product of its sides

i.e. area = side × side

So,

Area = (3p+5q) × (5p-7q)

= 3p (5p -7q) + 5q(5p-7q)

= 15p

^{2}- 21pq + 25pq - 35q^{2}= 15p

^{2}+ 4pq - 35q^{2}sq. units- Final Answer:

^{2}+ 4pq - 35q^{2}sq. units.Maths-

### Find the error in the given statement.

All monomials with the same degree are like terms.

Explanation:

We have given a statement all monomials with the same degree are like terms.

The above statement is not true always.

The variable should also be same.

Example:4x, 5y

Here both have degree one and both are monomials,

But since, The variables are not same they are not like terms.

- We have been given a statement in the question for which we have to find the error in the given statement.

We have given a statement all monomials with the same degree are like terms.

The above statement is not true always.

The variable should also be same.

Example:4x, 5y

Here both have degree one and both are monomials,

But since, The variables are not same they are not like terms.

### Find the error in the given statement.

All monomials with the same degree are like terms.

Maths-General

Explanation:

We have given a statement all monomials with the same degree are like terms.

The above statement is not true always.

The variable should also be same.

Example:4x, 5y

Here both have degree one and both are monomials,

But since, The variables are not same they are not like terms.

- We have been given a statement in the question for which we have to find the error in the given statement.

We have given a statement all monomials with the same degree are like terms.

The above statement is not true always.

The variable should also be same.

Example:4x, 5y

Here both have degree one and both are monomials,

But since, The variables are not same they are not like terms.

Maths-

### Write equation of the line containing (-3, 4) and (-1, -2)

Hint:

We are given two points and we need to find the equation of the line passing through them. Recall that the equation of a line passing through two points (a, b) and (c, d) is given by

Step by step solution:

Let the given points be denoted by

(a, b) = (-3, 4)

(c, d) = (-1, -2)

The equation of a line passing through two points (a, b) and (c, d) is

Using the above points, we have

Simplifying the above equation, we have

Cross multiplying, we get

2(y + 2) = -6(x + 1)

Expanding the factors, we have

2y + 4 = -6x - 6

Taking all the terms in the left hand side, we have

6x + 2y + 4 + 6 = 0

Finally, the equation of the line is

6x + 2y + 10 = 0

Dividing the equation throughout by2, we get

3x + y + 5 = 0

This is the general form of the equation.

This is also the required equation.

Note:

We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.

We are given two points and we need to find the equation of the line passing through them. Recall that the equation of a line passing through two points (a, b) and (c, d) is given by

Step by step solution:

Let the given points be denoted by

(a, b) = (-3, 4)

(c, d) = (-1, -2)

The equation of a line passing through two points (a, b) and (c, d) is

Using the above points, we have

Simplifying the above equation, we have

Cross multiplying, we get

2(y + 2) = -6(x + 1)

Expanding the factors, we have

2y + 4 = -6x - 6

Taking all the terms in the left hand side, we have

6x + 2y + 4 + 6 = 0

Finally, the equation of the line is

6x + 2y + 10 = 0

Dividing the equation throughout by2, we get

3x + y + 5 = 0

This is the general form of the equation.

This is also the required equation.

Note:

We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.

### Write equation of the line containing (-3, 4) and (-1, -2)

Maths-General

Hint:

We are given two points and we need to find the equation of the line passing through them. Recall that the equation of a line passing through two points (a, b) and (c, d) is given by

Step by step solution:

Let the given points be denoted by

(a, b) = (-3, 4)

(c, d) = (-1, -2)

The equation of a line passing through two points (a, b) and (c, d) is

Using the above points, we have

Simplifying the above equation, we have

Cross multiplying, we get

2(y + 2) = -6(x + 1)

Expanding the factors, we have

2y + 4 = -6x - 6

Taking all the terms in the left hand side, we have

6x + 2y + 4 + 6 = 0

Finally, the equation of the line is

6x + 2y + 10 = 0

Dividing the equation throughout by2, we get

3x + y + 5 = 0

This is the general form of the equation.

This is also the required equation.

Note:

We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.

We are given two points and we need to find the equation of the line passing through them. Recall that the equation of a line passing through two points (a, b) and (c, d) is given by

Step by step solution:

Let the given points be denoted by

(a, b) = (-3, 4)

(c, d) = (-1, -2)

The equation of a line passing through two points (a, b) and (c, d) is

Using the above points, we have

Simplifying the above equation, we have

Cross multiplying, we get

2(y + 2) = -6(x + 1)

Expanding the factors, we have

2y + 4 = -6x - 6

Taking all the terms in the left hand side, we have

6x + 2y + 4 + 6 = 0

Finally, the equation of the line is

6x + 2y + 10 = 0

Dividing the equation throughout by2, we get

3x + y + 5 = 0

This is the general form of the equation.

This is also the required equation.

Note:

We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.

Maths-

### Simplify and write the polynomial in its standard form.

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

### Simplify and write the polynomial in its standard form.

Maths-General

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

Maths-

### What must be added to x^{3}+3x-8 to get 3x^{3}+x^{2}+6?

Answer:

○ Always take like terms together while performing addition.

○ In addition to polynomials only terms with the same coefficient are added.

Sum: 3x

Term : x

○ Step 1:

○ Let A must be added to get 3x

So,

A + x

A = (3x

A = 3x

A = 3x

A = 2x

- Hint:

○ Always take like terms together while performing addition.

○ In addition to polynomials only terms with the same coefficient are added.

- Step by step explanation:

Sum: 3x

^{3 }+ x^{2 }+ 6Term : x

^{3 }+ 3x - 8○ Step 1:

○ Let A must be added to get 3x

^{3 }+ x^{2 }+ 6.So,

A + x

^{3 }+ 3x - 8 = 3x^{3 }+ x^{2 }+ 6A = (3x

^{3 }+ x^{2 }+ 6 ) - (x^{3 }+ 3x - 8)A = 3x

^{3 }+ x^{2 }+ 6 - x^{3 }- 3x + 8A = 3x

^{3}- x^{3 }+ x^{2 }- 3x+ 6 + 8A = 2x

^{3 }+ x^{2 }- 3x+ 14- Final Answer:

^{3 }+ x^{2 }- 3x+ 14.### What must be added to x^{3}+3x-8 to get 3x^{3}+x^{2}+6?

Maths-General

Answer:

○ Always take like terms together while performing addition.

○ In addition to polynomials only terms with the same coefficient are added.

Sum: 3x

Term : x

○ Step 1:

○ Let A must be added to get 3x

So,

A + x

A = (3x

A = 3x

A = 3x

A = 2x

- Hint:

○ Always take like terms together while performing addition.

○ In addition to polynomials only terms with the same coefficient are added.

- Step by step explanation:

Sum: 3x

^{3 }+ x^{2 }+ 6Term : x

^{3 }+ 3x - 8○ Step 1:

○ Let A must be added to get 3x

^{3 }+ x^{2 }+ 6.So,

A + x

^{3 }+ 3x - 8 = 3x^{3 }+ x^{2 }+ 6A = (3x

^{3 }+ x^{2 }+ 6 ) - (x^{3 }+ 3x - 8)A = 3x

^{3 }+ x^{2 }+ 6 - x^{3 }- 3x + 8A = 3x

^{3}- x^{3 }+ x^{2 }- 3x+ 6 + 8A = 2x

^{3 }+ x^{2 }- 3x+ 14- Final Answer:

^{3 }+ x^{2 }- 3x+ 14.Maths-

### Simplify and write the polynomial in its standard form.

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

### Simplify and write the polynomial in its standard form.

Maths-General

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

Maths-

### Write the polynomial in its standard form.

Explanation:

We have given a polynomial

We know that the terms are written in descending order of their degree.

So, In Standard form

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form.

We have given a polynomial

We know that the terms are written in descending order of their degree.

So, In Standard form

### Write the polynomial in its standard form.

Maths-General

Explanation:

We have given a polynomial

We know that the terms are written in descending order of their degree.

So, In Standard form

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form.

We have given a polynomial

We know that the terms are written in descending order of their degree.

So, In Standard form

Maths-

### Name the polynomial based on its degree and number of terms.

- We have been given a function in the question
- We will have to name the polynomial based on its degree and number of terms.

We have given a polynomial

Its degree is 1 and contain one variable

This is linear polynomial

### Name the polynomial based on its degree and number of terms.

Maths-General

- We have been given a function in the question
- We will have to name the polynomial based on its degree and number of terms.

We have given a polynomial

Its degree is 1 and contain one variable

This is linear polynomial

Maths-

### Show m = 2 for the straight line 8x - 4y = 12.

Hint:

We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.

Step by step solution:

The slope/ gradient of a line is denoted by m.

The given equation of the line is

8x - 4y = 12

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation 8x - 4y = 12, as below

-4y = -8x - 12

Dividing the above equation by (-4) throughout, we get

Simplifying, we have

y = 2x + 3

Comparing with y = mx + c, we get that m = 2

Thus, m = 2 for the straight line 8x - 4y = 12

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get

We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.

Step by step solution:

The slope/ gradient of a line is denoted by m.

The given equation of the line is

8x - 4y = 12

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation 8x - 4y = 12, as below

-4y = -8x - 12

Dividing the above equation by (-4) throughout, we get

Simplifying, we have

y = 2x + 3

Comparing with y = mx + c, we get that m = 2

Thus, m = 2 for the straight line 8x - 4y = 12

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get

### Show m = 2 for the straight line 8x - 4y = 12.

Maths-General

Hint:

We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.

Step by step solution:

The slope/ gradient of a line is denoted by m.

The given equation of the line is

8x - 4y = 12

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation 8x - 4y = 12, as below

-4y = -8x - 12

Dividing the above equation by (-4) throughout, we get

Simplifying, we have

y = 2x + 3

Comparing with y = mx + c, we get that m = 2

Thus, m = 2 for the straight line 8x - 4y = 12

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get

We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.

Step by step solution:

The slope/ gradient of a line is denoted by m.

The given equation of the line is

8x - 4y = 12

We convert this equation in the slope intercept form, which is

y = mx + c

Where m is the slope of the line and c is the y-intercept.

We rewrite the equation 8x - 4y = 12, as below

-4y = -8x - 12

Dividing the above equation by (-4) throughout, we get

Simplifying, we have

y = 2x + 3

Comparing with y = mx + c, we get that m = 2

Thus, m = 2 for the straight line 8x - 4y = 12

Note:

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept = , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get

Maths-

### Simplify. Write each answer in its standard form.

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form.

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

### Simplify. Write each answer in its standard form.

Maths-General

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form.

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

Maths-

### Simplify. Write each answer in its standard form.

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form.

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be

### Simplify. Write each answer in its standard form.

Maths-General

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be

- We have been given a function in the question.
- We will have to simplify it and further write the answer in its standard form.

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be

Maths-

### Simplify -6 + 4a^{2 }+ 2b^{2} - 7xz - 3xz + 4a^{2 }- 5b^{2 }- 2.

Answer:

○ Like terms are those whose coefficients are the same.

○ Perform basic arithmetic operations on like terms.

Expression: -6 + 4a

○ Step 1:

○ Group like terms.

-6 + 4a

( -6 - 2) + (4a

( -8) + (8a

8a

- Hint:

○ Like terms are those whose coefficients are the same.

○ Perform basic arithmetic operations on like terms.

- Step by step explanation:

Expression: -6 + 4a

^{2 }+ 2b^{2}- 7xz - 3xz + 4a^{2 }- 5b^{2 }- 2.○ Step 1:

○ Group like terms.

-6 + 4a

^{2 }+ 2b^{2}- 7xz - 3xz + 4a^{2 }- 5b^{2 }- 2( -6 - 2) + (4a

^{2 }+ 4a^{2}) - (7xz + 3xz) + (2b^{2}- 5b^{2 })( -8) + (8a

^{2}) - (10xz ) + (- 3b^{2 })8a

^{2 }- 3b^{2}- 10xz - 8- Final Answer:

^{2 }- 3b^{2}- 10xz - 8.### Simplify -6 + 4a^{2 }+ 2b^{2} - 7xz - 3xz + 4a^{2 }- 5b^{2 }- 2.

Maths-General

Answer:

○ Like terms are those whose coefficients are the same.

○ Perform basic arithmetic operations on like terms.

Expression: -6 + 4a

○ Step 1:

○ Group like terms.

-6 + 4a

( -6 - 2) + (4a

( -8) + (8a

8a

- Hint:

○ Like terms are those whose coefficients are the same.

○ Perform basic arithmetic operations on like terms.

- Step by step explanation:

Expression: -6 + 4a

^{2 }+ 2b^{2}- 7xz - 3xz + 4a^{2 }- 5b^{2 }- 2.○ Step 1:

○ Group like terms.

-6 + 4a

^{2 }+ 2b^{2}- 7xz - 3xz + 4a^{2 }- 5b^{2 }- 2( -6 - 2) + (4a

^{2 }+ 4a^{2}) - (7xz + 3xz) + (2b^{2}- 5b^{2 })( -8) + (8a

^{2}) - (10xz ) + (- 3b^{2 })8a

^{2 }- 3b^{2}- 10xz - 8- Final Answer:

^{2 }- 3b^{2}- 10xz - 8.Maths-

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We have to simplify it and further writer it in its standard form.

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

Maths-General

Explanation:

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

- We have been given a function in the question.
- We have to simplify it and further writer it in its standard form.

We know that in polynomial we add/subtract like terms

So,

Now, We know that the terms are written in descending order of their degree.

So, In the standard form

The given polynomial will be .

Maths-

### The coordinate A=(0,2) lies on a straight line. The gradient of the line is 5 . Using this information, state the equation of the straight line.

Hint:

We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0

Step by step solution:

Given,

Slope/ Gradient of the line (m) = 5

Let (a, b) denote the point A lying on the plane.

Then (a, b) = (0, 2)

We know that, the equation of a line with slope m and passing through the point (a, b) is given by

y - b = m(x - a)

Putting the values of m and (a, b) in the above equation, we get

y - 2 = 5(x - 0)

Simplifying, we have

y - 2 = 5x

Taking all the terms on one side and rewriting the above equation, we have

5x - y + 2 = 0

This is the required equation of the line.

Note:

The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.

Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.

We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0

Step by step solution:

Given,

Slope/ Gradient of the line (m) = 5

Let (a, b) denote the point A lying on the plane.

Then (a, b) = (0, 2)

We know that, the equation of a line with slope m and passing through the point (a, b) is given by

y - b = m(x - a)

Putting the values of m and (a, b) in the above equation, we get

y - 2 = 5(x - 0)

Simplifying, we have

y - 2 = 5x

Taking all the terms on one side and rewriting the above equation, we have

5x - y + 2 = 0

This is the required equation of the line.

Note:

The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.

Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.

### The coordinate A=(0,2) lies on a straight line. The gradient of the line is 5 . Using this information, state the equation of the straight line.

Maths-General

Hint:

We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0

Step by step solution:

Given,

Slope/ Gradient of the line (m) = 5

Let (a, b) denote the point A lying on the plane.

Then (a, b) = (0, 2)

We know that, the equation of a line with slope m and passing through the point (a, b) is given by

y - b = m(x - a)

Putting the values of m and (a, b) in the above equation, we get

y - 2 = 5(x - 0)

Simplifying, we have

y - 2 = 5x

Taking all the terms on one side and rewriting the above equation, we have

5x - y + 2 = 0

This is the required equation of the line.

Note:

The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.

Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.

We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0

Step by step solution:

Given,

Slope/ Gradient of the line (m) = 5

Let (a, b) denote the point A lying on the plane.

Then (a, b) = (0, 2)

We know that, the equation of a line with slope m and passing through the point (a, b) is given by

y - b = m(x - a)

Putting the values of m and (a, b) in the above equation, we get

y - 2 = 5(x - 0)

Simplifying, we have

y - 2 = 5x

Taking all the terms on one side and rewriting the above equation, we have

5x - y + 2 = 0

This is the required equation of the line.

Note:

The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.

Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.