Question

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!!!

Answer 1

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.