Question

Which expression is a difference of squares with a factor of 5x − 8?

25x2 − 16
25x2 + 16
25x2 − 64
25x2 + 64

Answer 1

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

(5x-8)(5x+8) = 25x2 - 64

answer: 25x2 - 64

Answer 2

option (3) is correct.

`25x^2-64`

Explanation:

Given : factor 5x − 8

We have to choose an expression out of given option that is a difference of squares with a factor of 5x − 8

Using algebraic identity
`a^2-b^2=(a+b)(a-b)`

a difference of squares is written mathematically as
`a^2-b^2`

Since one factor is 5x − 8

using identity stated above other factor has be 5x+8

Thus
`(5x+8)(5x-8)`

On simplify , we get

`(5x+8)(5x-8)=(5x)^2-8^2=25x^2-64`

Thus, option (3) is correct.