Question

factor completely.
$9n^5 - 9n^4 - 6n^3 + 6n^2$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms: $(9n^5 - 9n^4) + (-6n^3 + 6n^2)$

Step2: Factor out GCF from each group

Factor out $9n^4$ from the first group and $-6n^2$ from the second group: $9n^4(n - 1) - 6n^2(n - 1)$

Step3: Factor out the common binomial factor

Factor out $(n - 1)$: $(n - 1)(9n^4 - 6n^2)$

Step4: Factor out GCF from the quadratic factor

Factor out $3n^2$ from $9n^4 - 6n^2$: $3n^2(n - 1)(3n^2 - 2)$

Answer:

$3n^2(n - 1)(3n^2 - 2)$