Answer to Question #173795 in Physics for Festus

Question

Factorize x⁴ - 16

Answer 1

$$x⁴ - 16=(x^2)^2-(2^2)^2.$$

We know that

$$a^2-b^2=(a-b)(a+b).$$

Thus, putting

$$a=x^2, b=2^2,$$

we have

$$x⁴ - 16=(x^2)^2-(2^2)^2=(x^2-2^2)(x^2+2^2).$$

Apply the rule for $x^2-2^2$:

$$(x^2-2^2)=((x-2)(x+2)).$$

Therefore,

$$x⁴ - 16=(x-2)(x+2)(x^2+4)$$