Question

14/22
factor completely:
$x^4-9x^2$
hint: factor gcf first.
$(x^2+3x)(x^2-3x)$
$(x^2+9)(x-3)(x+3)$
$x^2(x+3)(x-3)$
$x^2(x^2-9)$

Explanation:

Step1: Factor out the GCF

The greatest common factor of $x^4$ and $9x^2$ is $x^2$.
$x^4 - 9x^2 = x^2(x^2 - 9)$

Step2: Factor the difference of squares

$x^2 - 9$ is a difference of squares ($a^2 - b^2 = (a-b)(a+b)$ where $a=x$, $b=3$).
$x^2(x^2 - 9) = x^2(x-3)(x+3)$

Answer:

$x^2(x+3)(x-3)$