Question

#12 \\(\left(9n^{4} - 6n^{3}\
ight)\div\left(27n^{2} + 18n\
ight)\\)

Explanation:

Step1: Factor out common terms

Factor $3n^3$ from first binomial, $9n$ from second:
$3n^3(3n - 2) - 9n(3n - 2)$

Step2: Factor out shared binomial

Factor $(3n - 2)$ from both terms:
$(3n - 2)(3n^3 - 9n)$

Step3: Factor remaining term fully

Factor $3n$ from the second binomial:
$(3n - 2) \cdot 3n(n^2 - 3)$

Step4: Rearrange factors for clarity

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

Answer:

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