Question

URGENT Help ! ! Deion was asked to completely factor the expression 10x^4−160.

Deion's answer was the following:


10(x^4−16)

10(x^2+4) (x^2−4)

Has Deion completely factored the expression? If yes, explain how you know. If not, explain what step Deion missed and what the correct solution would be.

Answer 1

Using subtraction of perfect squares, it is found that Deion missed the subtraction of perfect squares at the term ((x^2−4), and the correct solution would be given by:

$10(x^2 + 4)(x + 2)(x - 2)$

What is subtraction of perfect squares?

The factoring is represented by the following identity:

$a^2 - b^2 = (a - b)(a + b)$

In this problem, the expression is:

$10x^4 - 160$

The common term is 10, hence:

$10(x^4 - 16)$

Both $x^4$ and 16 are perfect squares, hence:

$x^4 - 16 = (x^2)^2 - 4^2 = (x^2 - 4)(x^2 + 4)$

$x^2$ and 4 are perfect squares, hence:

$x^2 - 4 = x^2 - 2^2 = (x + 2)(x - 2)$

This last step was missed by Deion, hence the factored expression is:

$10(x^2 + 4)(x + 2)(x - 2)$

To learn more about subtraction of perfect squares, you can check https://brainly.com/question/16948935