Thread: How do you factor x^4-16?

My answer sheet says =(x²)²-(2²)²
= (x²-2²)(x²+2²)
=(x-2)(x+2)(x²+2)
My question is, how did it break that down like that?

Originally Posted by EJdive43

My answer sheet says =(x²)²-(2²)²
= (x²-2²)(x²+2²)
=(x-2)(x+2)(x²+2)
My question is, how did it break that down like that?

Difference of squares

x^4 - 16

This is the difference of two squares, which factors to
(x^2 + 4)(x^2 - 4)

You can't factor x^2 + 4 anymore, but x^2 - 4 is another difference of squares, which can be factored to (x + 2)(x - 2), the final answer is

(x^2 + 4)(x + 2)(x - 2)