i don't understand what to do with this problem?

Question

Factor the polynomial completely.

a⁴−1

Answer 1

What we have here is a difference of two squares.

a² * a² = a⁴

1 * 1 = 1

 

A difference of two squares quickly factors into:

a² - b² = (a + b)(a - b)

So applying that here gives us:

(a² + 1)(a² - 1)

 

Now take a look at the second set of parentheses. There too is a Do2S:

a * a = a²

So we repeat the process again:

(a² + 1)(a + 1)(a - 1)

 

a² + 1 doesn't factor at all, so we're now done.

Answer 2

It's

 

(a^2-1)(a^2+1)=(a-1)(a+1)(a^2+1)