Question

The polynomial is a difference squares. Use the formula a^2 -b^2=(a+b)(a-b) to factor completely. 81x^2-49 the value of a is the value of b is the product of the prime factors is

Answer 1

(9x+7)(9x-7)

Explanation:

We have given an expression.

81x²-49

We have to use difference formula which is given in question.

a²-b² =(a+b)(a-b)

We have to write given expression in above formula.

81x²-49 = (9x)²-(7)²

Using given formula , we have

81x²-49 = (9x+7)(9x-7)

Hence, the factors of given expression are (9x-7) and (9x+7).

Answer 2

Answer:
`(9x)^(2)-(7)^(2)=(9x-7)(9x+7)`

Explanation:

1. By definition you have that the difference of squares is:

`a^(2)-b^(2)=(a+b)(a-b)`

2. Given the polynomial:

`81x^(2)-49`

You can identify that there are two terms whose signs are different and they are perfect squares.

3. Therefore, you have:

`81x^(2)-49=(9x)^(2)-(7)^(2)=(9x-7)(9x+7)`