Question

What is the factored form of 216p^3+125q^3?

Answer 1

Notice that 216 is a perfect cube and so is 125.
You have the sum of two cubes which is factorable and follows the pattern:

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

$216p^3 + 125q^3 =$

$= (6p)^3 + (5q)^3$

$= (6p + 5q)(36p^2 - 30pq + 25q^2)$