Maths-
General
Easy
Question
What is the total area of four white triangles if 𝑥 = 12 𝑐𝑚?
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
Area of a square = (side)2
The correct answer is: 180 cm2.
The area of the outer square of side x+6 cm = (x+6)2
(x+6)2 = (x+6)(x+6) = x(x+6) +6(x+6)
= x(x) + x(6) +6(x) +6(6)
= x2 + 6x + 6x + 36
= x2 + 12x + 36
The area of the inner square of side x cm = x2
Now, Total area of four white triangles = Area of the outer square - area of the inner square
= x2 + 12x + 36 - x2
= 12x + 36
Given that x =12 cm
So, Total area of four white triangles = 12(12) + 36
= 144 + 36 = 180 cm2
Final Answer:
Hence, the total area of four white triangles is 180 cm2.
The area of the inner square of side x cm = x2
Now, Total area of four white triangles = Area of the outer square - area of the inner square
Given that x =12 cm
So, Total area of four white triangles = 12(12) + 36
Final Answer:
Hence, the total area of four white triangles is 180 cm2.
Related Questions to study
Maths-
Describe the possible values of x.
Answer:
b < a + c
c < a + b
a = x + 11, b = 2x + 10, and c = 5x - 9.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
x + 11 < 7x + 1,
11 – 1 < 7x - x
10 < 6x
1.6 < x
Now, consider,
3x - 19 < x + 11
3x - x < 11 + 19
2x < 30
x < 15
therefore,
1.6 < x < 15
x < 15
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
b < a + c
c < a + b
- Step-by-step explanation:
- Given:
a = x + 11, b = 2x + 10, and c = 5x - 9.
- Step 1:
- First check validity.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
- Step 1:
- First check validity.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
- Step 1:
- First check validity.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
x + 11 < 7x + 1,
11 – 1 < 7x - x
10 < 6x
1.6 < x
Now, consider,
3x - 19 < x + 11
3x - x < 11 + 19
2x < 30
x < 15
therefore,
1.6 < x < 15
x < 15
- Final Answer:
Describe the possible values of x.
Maths-General
Answer:
b < a + c
c < a + b
a = x + 11, b = 2x + 10, and c = 5x - 9.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
x + 11 < 7x + 1,
11 – 1 < 7x - x
10 < 6x
1.6 < x
Now, consider,
3x - 19 < x + 11
3x - x < 11 + 19
2x < 30
x < 15
therefore,
1.6 < x < 15
x < 15
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
b < a + c
c < a + b
- Step-by-step explanation:
- Given:
a = x + 11, b = 2x + 10, and c = 5x - 9.
- Step 1:
- First check validity.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
- Step 1:
- First check validity.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
- Step 1:
- First check validity.
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
x + 11 < 7x + 1,
11 – 1 < 7x - x
10 < 6x
1.6 < x
Now, consider,
3x - 19 < x + 11
3x - x < 11 + 19
2x < 30
x < 15
therefore,
1.6 < x < 15
x < 15
- Final Answer:
Maths-
What expression represents the total area of the four white triangles?
The area of the outer square of side x+6 cm = (x+6)2
(x+6)2 = (x+6)(x+6) = x(x+6) +6(x+6)
= x(x) + x(6) +6(x) +6(6)
= x2 + 6x + 6x + 36
= x2 + 12x + 36
The area of the inner square of side x cm = x2
Now, Total area of four white triangles = Area of the outer square - area of the inner square
= x2 + 12x + 36 - x2
= 12x + 36
Final Answer:
Hence, the expression for the total area of the four white triangles is 12x + 36.
What expression represents the total area of the four white triangles?
Maths-General
The area of the outer square of side x+6 cm = (x+6)2
(x+6)2 = (x+6)(x+6) = x(x+6) +6(x+6)
= x(x) + x(6) +6(x) +6(6)
= x2 + 6x + 6x + 36
= x2 + 12x + 36
The area of the inner square of side x cm = x2
Now, Total area of four white triangles = Area of the outer square - area of the inner square
= x2 + 12x + 36 - x2
= 12x + 36
Final Answer:
Hence, the expression for the total area of the four white triangles is 12x + 36.
Maths-
Write the product in the standard form. (𝑥2 − 2𝑦)(𝑥2 + 2𝑦)
(x2 − 2y)(x2 + 2y) = x2(x2 + 2y) - 2y(x2 + 2y)
= x2(x2) + x2(2y) - 2y(x2) - 2y(2y)
= x4 + 2x2y - 2x2y - 4y2
= x4 - 4y2
Final Answer:
Hence, the simplified form of (𝑥2 − 2𝑦)(𝑥2 + 2𝑦) is x4 - 4y2.
Write the product in the standard form. (𝑥2 − 2𝑦)(𝑥2 + 2𝑦)
Maths-General
(x2 − 2y)(x2 + 2y) = x2(x2 + 2y) - 2y(x2 + 2y)
= x2(x2) + x2(2y) - 2y(x2) - 2y(2y)
= x4 + 2x2y - 2x2y - 4y2
= x4 - 4y2
Final Answer:
Hence, the simplified form of (𝑥2 − 2𝑦)(𝑥2 + 2𝑦) is x4 - 4y2.
Maths-
Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)
(x − 2.5)(x + 2.5) = (x − 
)(x + )
)(x + )= x(x + ) - (x + )
= x(x) + x() - (x) - ()
= x2 + x - x -
= x2 -
= x2 - 6.25
Final Answer:
Hence, the simplified form of (𝑥 − 2.5)(𝑥 + 2.5) is x2 - 6.25.
Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)
Maths-General
(x − 2.5)(x + 2.5) = (x − )(x + )
)(x + )= x(x + ) - (x + )
= x(x) + x() - (x) - ()
= x2 + x - x -
= x2 -
= x2 - 6.25
Final Answer:
Hence, the simplified form of (𝑥 − 2.5)(𝑥 + 2.5) is x2 - 6.25.
Maths-
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
5 inches, 12 inches
Answer:
c < a + b
a = 5 inches, b = 12 inches.
a = 5 inches, b = 12 inches.
c < a + b
∴ c < 5 + 12
c < 17
c < a + b
∴ c < 5 + 12
c < 17
12 – 5 < c < 5 + 12
7 < c < 17
Hence, all numbers between 7 and 17 will be the length of third side.
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
c < a + b
- while finding possible lengths of third side use below formula
- Step-by-step explanation:
- Given:
a = 5 inches, b = 12 inches.
- Step-by-step explanation:
- Given:
a = 5 inches, b = 12 inches.
- Step 1:
- Find length of third side.
c < a + b
∴ c < 5 + 12
c < 17
- Step 1:
- Find length of third side.
c < a + b
∴ c < 5 + 12
c < 17
- Step 2:
- Step 2:
12 – 5 < c < 5 + 12
7 < c < 17
Hence, all numbers between 7 and 17 will be the length of third side.
- Final Answer:
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
5 inches, 12 inches
Maths-General
Answer:
c < a + b
a = 5 inches, b = 12 inches.
a = 5 inches, b = 12 inches.
c < a + b
∴ c < 5 + 12
c < 17
c < a + b
∴ c < 5 + 12
c < 17
12 – 5 < c < 5 + 12
7 < c < 17
Hence, all numbers between 7 and 17 will be the length of third side.
- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
c < a + b
- while finding possible lengths of third side use below formula
- Step-by-step explanation:
- Given:
a = 5 inches, b = 12 inches.
- Step-by-step explanation:
- Given:
a = 5 inches, b = 12 inches.
- Step 1:
- Find length of third side.
c < a + b
∴ c < 5 + 12
c < 17
- Step 1:
- Find length of third side.
c < a + b
∴ c < 5 + 12
c < 17
- Step 2:
- Step 2:
12 – 5 < c < 5 + 12
7 < c < 17
Hence, all numbers between 7 and 17 will be the length of third side.
- Final Answer:
Maths-
Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)
(3a − 4b)(3a + 4b) = 3a(3a + 4b) - 4b(3a + 4b)
= 3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
= 9a2 + 12ab - 12ab - 16b2
= 9a2 - 16b2
Final Answer:
Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
= 3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
= 9a2 + 12ab - 12ab - 16b2
= 9a2 - 16b2
Final Answer:
Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)
Maths-General
(3a − 4b)(3a + 4b) = 3a(3a + 4b) - 4b(3a + 4b)
= 3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
= 9a2 + 12ab - 12ab - 16b2
= 9a2 - 16b2
Final Answer:
Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
= 3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
= 9a2 + 12ab - 12ab - 16b2
= 9a2 - 16b2
Final Answer:
Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
Maths-
Write the product in the standard form. 
Final Answer:
Hence, the simplified form of 
.
Write the product in the standard form.
Maths-General
Final Answer:
Hence, the simplified form of .
Maths-
How is it possible that the sum of two quadratic trinomials is a linear binomial?
Explanation:
it is possible that the sum of two quadratic trinomials is a linear binomial
If the other terms get cancel
Example:
,
On addition we will get
, which is a linear binomial.
- We have to find out how is it possible that the sum of two quadratic trinomials is a linear binomial.
it is possible that the sum of two quadratic trinomials is a linear binomial
If the other terms get cancel
Example:
,On addition we will get
, which is a linear binomial.How is it possible that the sum of two quadratic trinomials is a linear binomial?
Maths-General
Explanation:
it is possible that the sum of two quadratic trinomials is a linear binomial
If the other terms get cancel
Example:
,
On addition we will get, which is a linear binomial.
- We have to find out how is it possible that the sum of two quadratic trinomials is a linear binomial.
it is possible that the sum of two quadratic trinomials is a linear binomial
If the other terms get cancel
Example:
,On addition we will get
, which is a linear binomial.Maths-
If (3x-4) (5x+7) = 15x2-ax-28, so find the value of a?
Answer:
○ Two terms.
(3x-4) (5x+7) = 15x2-ax-28
○ Step 1:
○ Simplify the right side:
○ (3x-4) (5x+7)
3x(5x+7) - 4(5x+7)
15x2 + 21x - 20x - 28
15x2 + x - 28
○ Step 1:
○ compare both side:
15x2 + x - 28 =15x2- ax - 28
By comparing we get
a = -1
- Hint:
- Step by step explanation:
○ Two terms.
(3x-4) (5x+7) = 15x2-ax-28
○ Step 1:
○ Simplify the right side:
○ (3x-4) (5x+7)
3x(5x+7) - 4(5x+7)15x2 + 21x - 20x - 2815x2 + x - 28○ Step 1:
○ compare both side:
15x2 + x - 28 =15x2- ax - 28
By comparing we get
a = -1
- Final Answer:
If (3x-4) (5x+7) = 15x2-ax-28, so find the value of a?
Maths-General
Answer:
○ Two terms.
(3x-4) (5x+7) = 15x2-ax-28
○ Step 1:
○ Simplify the right side:
○ (3x-4) (5x+7)
3x(5x+7) - 4(5x+7)
15x2 + 21x - 20x - 28
15x2 + x - 28
○ Step 1:
○ compare both side:
15x2 + x - 28 =15x2- ax - 28
By comparing we get
a = -1
- Hint:
- Step by step explanation:
○ Two terms.
(3x-4) (5x+7) = 15x2-ax-28
○ Step 1:
○ Simplify the right side:
○ (3x-4) (5x+7)
3x(5x+7) - 4(5x+7)15x2 + 21x - 20x - 2815x2 + x - 28○ Step 1:
○ compare both side:
15x2 + x - 28 =15x2- ax - 28
By comparing we get
a = -1
- Final Answer:
Maths-
The difference of x4+2x2-3x+7 and another polynomial is x3+x2+x-1. What is the
another polynomial?
Answer:
○ Always take like terms together while performing subtraction.
○ In addition to polynomials only terms with the same coefficient are subtracted.
One polynomial: x4+2x2-3x+7
Difference: x3+x2+x-1.
○ Step 1:
○ Let another polynomial be A.
So,
(x4+2x2-3x+7) – A = (x3+x2+x-1)
A = (x4+2x2-3x+7) - (x3+x2+x-1)
A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1
A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1
A = x4 - x3 + x2 - 4x + 8
- Hint:
○ Always take like terms together while performing subtraction.
○ In addition to polynomials only terms with the same coefficient are subtracted.
- Step by step explanation:
One polynomial: x4+2x2-3x+7
Difference: x3+x2+x-1.
○ Step 1:
○ Let another polynomial be A.
So,
(x4+2x2-3x+7) – A = (x3+x2+x-1)A = (x4+2x2-3x+7) - (x3+x2+x-1) A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1 A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1 A = x4 - x3 + x2 - 4x + 8- Final Answer:
The difference of x4+2x2-3x+7 and another polynomial is x3+x2+x-1. What is the
another polynomial?
Maths-General
Answer:
○ Always take like terms together while performing subtraction.
○ In addition to polynomials only terms with the same coefficient are subtracted.
One polynomial: x4+2x2-3x+7
Difference: x3+x2+x-1.
○ Step 1:
○ Let another polynomial be A.
So,
(x4+2x2-3x+7) – A = (x3+x2+x-1)
A = (x4+2x2-3x+7) - (x3+x2+x-1)
A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1
A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1
A = x4 - x3 + x2 - 4x + 8
- Hint:
○ Always take like terms together while performing subtraction.
○ In addition to polynomials only terms with the same coefficient are subtracted.
- Step by step explanation:
One polynomial: x4+2x2-3x+7
Difference: x3+x2+x-1.
○ Step 1:
○ Let another polynomial be A.
So,
(x4+2x2-3x+7) – A = (x3+x2+x-1)A = (x4+2x2-3x+7) - (x3+x2+x-1) A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1 A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1 A = x4 - x3 + x2 - 4x + 8- Final Answer:
Maths-
Use the product of sum and difference to find 83 × 97.
83 can be written as (90 - 7) and 97 can be written as (90 + 7)
So, 83 × 97 can be written (90 - 7) × (90 + 7)
(90 - 7) × (90 + 7) = 90(90 + 7) - 7(90 + 7)
So, 83 × 97 can be written (90 - 7) × (90 + 7)
(90 - 7) × (90 + 7) = 90(90 + 7) - 7(90 + 7)
= 90(90) + 90(7) - 7(90) - 7(7)
= 8100 + 630 - 630 - 49
= 8100 - 49
= 8051
Final Answer:
Hence, the simplified form of 83 × 97 is 8051.
Use the product of sum and difference to find 83 × 97.
Maths-General
83 can be written as (90 - 7) and 97 can be written as (90 + 7)
So, 83 × 97 can be written (90 - 7) × (90 + 7)
(90 - 7) × (90 + 7) = 90(90 + 7) - 7(90 + 7)
So, 83 × 97 can be written (90 - 7) × (90 + 7)
(90 - 7) × (90 + 7) = 90(90 + 7) - 7(90 + 7)
= 90(90) + 90(7) - 7(90) - 7(7)
= 8100 + 630 - 630 - 49
= 8100 - 49
= 8051
Final Answer:
Hence, the simplified form of 83 × 97 is 8051.
Maths-
Determine the gradient and y-intercept from the following equation: 4x + y = -10
Hint:
Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
Step by step solution:
The given equation of the line is
4x + y = -10
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c, where m is the slope of the line and c is the y – intercept.
Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
y = -4x - 10
Comparing the above equation with y = mx + c, we get
m = -4 ;c = -10
Thus, we get
Gradient = -4
y-intercept = -10
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.
Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
Step by step solution:
The given equation of the line is
4x + y = -10
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c, where m is the slope of the line and c is the y – intercept.
Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
y = -4x - 10
Comparing the above equation with y = mx + c, we get
m = -4 ;c = -10
Thus, we get
Gradient = -4
y-intercept = -10
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.Determine the gradient and y-intercept from the following equation: 4x + y = -10
Maths-General
Hint:
Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
Step by step solution:
The given equation of the line is
4x + y = -10
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c, where m is the slope of the line and c is the y – intercept.
Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
y = -4x - 10
Comparing the above equation with y = mx + c, we get
m = -4 ;c = -10
Thus, we get
Gradient = -4
y-intercept = -10
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.
Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
Step by step solution:
The given equation of the line is
4x + y = -10
We need to convert this equation in the slope-intercept form of the line, which is
y = mx + c, where m is the slope of the line and c is the y – intercept.
Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
y = -4x - 10
Comparing the above equation with y = mx + c, we get
m = -4 ;c = -10
Thus, we get
Gradient = -4
y-intercept = -10
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.Maths-
Use the product of sum and difference to find 32 × 28.
32 can be written as (30 + 2) and 28 can be written as (30 - 2)
So, 32 × 28 can be written (30 + 2) × (30 - 2)
(30 + 2) × (30 - 2) = 30(30 - 2) + 2(30 - 2)
So, 32 × 28 can be written (30 + 2) × (30 - 2)
(30 + 2) × (30 - 2) = 30(30 - 2) + 2(30 - 2)
= 30(30) + 30(-2) + 2(30) + 2(-2)
= 900 - 60 + 60 - 4
= 900 - 4
= 896
Final Answer:
Hence, the simplified form of 32 × 28 is 896.
Use the product of sum and difference to find 32 × 28.
Maths-General
32 can be written as (30 + 2) and 28 can be written as (30 - 2)
So, 32 × 28 can be written (30 + 2) × (30 - 2)
(30 + 2) × (30 - 2) = 30(30 - 2) + 2(30 - 2)
So, 32 × 28 can be written (30 + 2) × (30 - 2)
(30 + 2) × (30 - 2) = 30(30 - 2) + 2(30 - 2)
= 30(30) + 30(-2) + 2(30) + 2(-2)
= 900 - 60 + 60 - 4
= 900 - 4
= 896
Final Answer:
Hence, the simplified form of 32 × 28 is 896.
Maths-
The sum of two expressions is x3-x2+3x-2. If one of them is x2 + 5x - 6, what is the
other?
Answer:
○ Always take like terms together while performing addition.
○ In subtraction of polynomials only coefficients are subtracted.
Sum: x3 -x2 + 3x- 2
Term: x2 + 5x- 6
○ Step 1:
○ Let the other term be A.
As given sum is x3 -x2 + 3x- 2
A + x2 + 5x- 6 = x3 -x2 + 3x- 2
A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 )
A = x3 -x2 + 3x - 2 - x2 - 5x + 6
A = x3 -x2 - x2 + 3x - 5x - 2 + 6
A = x3 -2x2 - 2x + 4
- Hint:
○ Always take like terms together while performing addition.
○ In subtraction of polynomials only coefficients are subtracted.
- Step by step explanation:
Sum: x3 -x2 + 3x- 2
Term: x2 + 5x- 6
○ Step 1:
○ Let the other term be A.
As given sum is x3 -x2 + 3x- 2
A + x2 + 5x- 6 = x3 -x2 + 3x- 2 A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 ) A = x3 -x2 + 3x - 2 - x2 - 5x + 6 A = x3 -x2 - x2 + 3x - 5x - 2 + 6 A = x3 -2x2 - 2x + 4- Final Answer:
The sum of two expressions is x3-x2+3x-2. If one of them is x2 + 5x - 6, what is the
other?
Maths-General
Answer:
○ Always take like terms together while performing addition.
○ In subtraction of polynomials only coefficients are subtracted.
Sum: x3 -x2 + 3x- 2
Term: x2 + 5x- 6
○ Step 1:
○ Let the other term be A.
As given sum is x3 -x2 + 3x- 2
A + x2 + 5x- 6 = x3 -x2 + 3x- 2
A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 )
A = x3 -x2 + 3x - 2 - x2 - 5x + 6
A = x3 -x2 - x2 + 3x - 5x - 2 + 6
A = x3 -2x2 - 2x + 4
- Hint:
○ Always take like terms together while performing addition.
○ In subtraction of polynomials only coefficients are subtracted.
- Step by step explanation:
Sum: x3 -x2 + 3x- 2
Term: x2 + 5x- 6
○ Step 1:
○ Let the other term be A.
As given sum is x3 -x2 + 3x- 2
A + x2 + 5x- 6 = x3 -x2 + 3x- 2 A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 ) A = x3 -x2 + 3x - 2 - x2 - 5x + 6 A = x3 -x2 - x2 + 3x - 5x - 2 + 6 A = x3 -2x2 - 2x + 4- Final Answer:
Maths-
Use the square of a binomial to find the value. 722
722 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 + 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 722 is 5184.
Use the square of a binomial to find the value. 722
Maths-General
722 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 + 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 722 is 5184.
