What is the completely factored form of 8x2 – 50?2(x + 5)(x – 5)2(2x – 5)(2x – 5)2(2x + 5)(2x + 5)2(2x + 5)(2x – 5)

ANSWER

The completely factored form is
[tex]2(2x + 5)(2x - 5)[/tex]

EXPLANATION

The given expression is
[tex]8 {x}^{2} - 50[/tex]

We factor the highest common factor to get,

[tex]2( {4x}^{2} - 25)[/tex]

We can rewrite the expression in the parenthesis as difference of two squares.

[tex]2( {(2x)}^{2} - {5}^{2} )[/tex]

Recall that,

[tex] {a}^{2} - {b}^{2} = (a + b)(a-b)[/tex]

This implies that,
[tex]2(2x + 5)(2x - 5)[/tex]

The correct answer is option D.