Question

How do you factor $x^4-16$?

Answer 1

$x^4-16=(x+2)(x-2)(x^2+4)$

Explanation:

Recall the factor of difference of square $a^2-b^2=(a-b)(a+b)$

We can re-write

$x^4-16={\left(x^2\right)}^2-4^2$

$\Rightarrow (x^2-4)(x^2+4)$

$\Rightarrow (x^2-2^2)(x+4)\Rightarrow$ difference of square again

$\Rightarrow (x-2)(x+2)(x+4)$