Question

Which of the following is the correct factorization of polynomial below? p^3-216q^3

Answer 1

Answer:

$(p-6q)(p^2+6pq+36pq^2)$

Step-by-step explanation:

$p^3-216q^3$

Rewrite $p^3-216q^3$ as $p^3-(6q)^3$:

$p^3-216q^3$

Rewrite 216 as $6^3$

$=p^3-6^3q^3$

Apply exponent rule: $a^mb^m=(ab)^m$

$6^3q^3=(6q)^3$

$=p^3-(6q)^3$

$=p^3-(6q)^3$

Apply difference of cubes formula: $x^3-y^3=(x-y)(x^2+xy+y^2)$

$p^3-(6q)^3=(p-6q)(p^2+6pq+6^2q^2)$

$=(p-6q)(p^2+6pq+6^2q^2)$

Refine.

$=(p-6q)(p^2+6pq+36q^2)$