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!!!

Respuesta :

Answer:

No. See below.

Step-by-step explanation:

[tex]( {x}^{4} - 1)[/tex]

Use the following formula (Difference of Two Squares)

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

[tex]( {x}^{4} - 1) = ( {x}^{2} + 1)( {x}^{2} - 1)[/tex]

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

[tex]( {x}^{2} + 1)(x + 1)(x - 1)[/tex]

This is the fully factored form.