Question

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 1

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

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) .

Answer 2

ANSWER

The completely factored form is

`2(2x + 5)(2x - 5)`

EXPLANATION

The given expression is

`8 {x}^(2) - 50`

We factor the highest common factor to get,


`2( {4x}^(2) - 25)`

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


`2( {(2x)}^(2) - {5}^(2) )`

Recall that,


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

This implies that,

`2(2x + 5)(2x - 5)`

The correct answer is option D.