Question

factor the following expression.
$15u^{9}v^{8}-24u^{6}v^{2}x^{3}$

Explanation:

Step1: Find the GCF of coefficients

The GCF of 15 and 24 is 3.

Step2: Find the GCF of variables with the same base

For $u$, the GCF of $u^{9}$ and $u^{6}$ is $u^{6}$ (using the rule $a^{m}\div a^{n}=a^{m - n}$, here $m\geq n$). For $v$, the GCF of $v^{8}$ and $v^{2}$ is $v^{2}$.

Step3: Factor out the GCF

$15u^{9}v^{8}-24u^{6}v^{2}x^{3}=3u^{6}v^{2}(5u^{3}v^{6} - 8x^{3})$

Answer:

$3u^{6}v^{2}(5u^{3}v^{6}-8x^{3})$