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.

Answer 1

Answer:

No. See below.

Step-by-step 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.