Question

Which product is equivalent to 25x2 – 16?

(5x − 4)(5x + 4)
(5x + 8)(5x − 8)
(5x − 4)(5x − 4)
(5x − 8)(5x − 8)

Answer 1

a

Explanation:

Answer 2

ANSWER

`25 {x}^(2) - 16 =( {5x - 4})(5x + 4)`

EXPLANATION

We want to factor the expression,


`25 {x}^(2) - 16`

We can rewrite the expression as


`25 {x}^(2) - 16 = ({5x})^(2) - {4}^(2)`

The expression is now a difference of two squares,

Recall that,


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

The expression now becomes;


`25 {x}^(2) - 16 =( {5x - 4})(5x + 4)`


Therefore the correct answer is option A.