Question

# What is the relationship between the sign of the binomial and the sign of the second term in the product?

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: binomial.

### Let’s say the binomial is a + b

If we find its square

(a + b)^{2} = (a + b)(a + b) = a(a + b) +b(a + b)

= a^{2} + ab + ab + b^{2}

= a^{2} + 2ab + b^{2}

Similarly if we take binomial a - b

If we find its square

(a - b)^{2} = (a-b)(a-b) = a(a-b) -b(a-b)

= a^{2} - ab - ab + b^{2}

= a^{2} - 2ab + b^{2}

So, from both the results we can see that the sign of second term in the product is same as the binomial.

Final Answer:

Hence, the sign of second term in the product is same as the binomial.

^{2}+ ab + ab + b

^{2}

^{2}+ 2ab + b

^{2}

Similarly if we take binomial a - b

If we find its square

^{2}= (a-b)(a-b) = a(a-b) -b(a-b)

^{2}- ab - ab + b

^{2}

^{2}- 2ab + b

^{2}

So, from both the results we can see that the sign of second term in the product is same as the binomial.

Final Answer:

Hence, the sign of second term in the product is same as the binomial.

### Related Questions to study

### Find the product. (2𝑥 − 1)^{2}

This question can be easily solved by using the formula

(a - b)2 = a2 - 2ab + b2

### Find the product. (2𝑥 − 1)^{2}

This question can be easily solved by using the formula

(a - b)2 = a2 - 2ab + b2

### The coefficient of 𝑥 in the product (𝑥 − 3) (𝑥 − 5) is

### The coefficient of 𝑥 in the product (𝑥 − 3) (𝑥 − 5) is

### Find the product. (𝑥 + 9)(𝑥 + 9)

This question can be easily solved by using the formula

(a + b)2 = a2 + 2ab + b2

### Find the product. (𝑥 + 9)(𝑥 + 9)

This question can be easily solved by using the formula

(a + b)2 = a2 + 2ab + b2

### Geeta spends 803.94 to buy a necklace and bracelet set for each of her friends. Each

necklace costs Rs 7.99 and each bracelet cost 5.89, how many necklace and bracelet

What sets did she buy?

### Geeta spends 803.94 to buy a necklace and bracelet set for each of her friends. Each

necklace costs Rs 7.99 and each bracelet cost 5.89, how many necklace and bracelet

What sets did she buy?

### Use either the square of a binomial or difference of squares to find the area of the square.

### Use either the square of a binomial or difference of squares to find the area of the square.

### Use a table to find the product.

(2𝑥 + 1) (4𝑥 + 1)

### Use a table to find the product.

(2𝑥 + 1) (4𝑥 + 1)

### Graph the equation on a coordinate plane.

### Graph the equation on a coordinate plane.

### Use a table to find the product.

(𝑥 − 6) (3𝑥 + 4)

### Use a table to find the product.

(𝑥 − 6) (3𝑥 + 4)

### Why the product of two binomials (𝑎 + 𝑏) and (𝑎 − 𝑏) is a binomial instead of a trinomial?

### Why the product of two binomials (𝑎 + 𝑏) and (𝑎 − 𝑏) is a binomial instead of a trinomial?

### Graph the equation

We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.

### Graph the equation

We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.

### The constant term in the product (𝑥 + 3) (𝑥 + 4) is

### The constant term in the product (𝑥 + 3) (𝑥 + 4) is

### Write the product in standard form. (3𝑦 − 5)(3𝑦 + 5)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in standard form. (3𝑦 − 5)(3𝑦 + 5)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in standard form. (𝑥 − 4)(𝑥 + 4)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in standard form. (𝑥 − 4)(𝑥 + 4)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2