Sinea thinks that the fully factored form of the expression (x^4-1) is (x^2-1)(x^2+1). Is she correct? Explain. I NEED THIS ASAP SOMEONE PLEASE HELP!!!

Question

asked Dec 6, 2022 102k views

1 Answer

Matthew Arkin · Answer 1 · 2022-12-09T16:45:17+0000

Answer:

No. See below.

Explanation:

$( {x}^(4) - 1)$

Use the following formula (Difference of Two Squares)

${x}^(2) - {y}^(2) = (x + y)(x - y)$

$( {x}^(4) - 1) = ( {x}^(2) + 1)( {x}^(2) - 1)$

We are not done yet. As we can still factor the expression which is x²-1 by using the same formula.

$( {x}^(2) + 1)(x + 1)(x - 1)$

This is the fully factored form.