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,

$x⁴ - 16=(x-2)(x+2)(x^2+4)$