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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.

Answer:

The factored form of 8x² – 50 is 2 (2x +5)(2x -5) .

Step-by-step explanation:

As given the expression in the question be as follow.

= 8x² - 50

= 2 (4x² - 25)

As

4x² = (2x)²

25 = 5²

Put above values in the expression

= 2 ((2x)² - 5²)

By using the property

(a² - b²) = (a + b)(a - b)

As

a = 2x

b = 5

Thus

= 2 (2x +5)(2x - 5)

Therefore the factored form of 8x² – 50 is 2 (2x +5)(2x -5) .