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:

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

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

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

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

Answer 2

Factored form involves factors who multiply themselves to make that expression or value.

The factored form of given expression is $(6p+5q)(36p^2 - 30pq + 25q^2)$

Given that:

• The expression:  $216p^3+125q^3$

To find:

The factored form of given expression.

Using the identity $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$:

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

since  $216p^3+125q^3 = (6p)^3 + (5q)^3$

Thus:

$\begin{aligned}216p^3+125q^3 &= (6p)^3 + (5q)^3\\ &= (6p + 5q)((6p)^2 - (6p)(5q) + (5q)^2))\\ &=(6p+5q)(36p^2 - 30pq + 25q^2) \end{aligned}$

Thus, the factored form of given expression is $(6p+5q)(36p^2 - 30pq + 25q^2)$

Learn more about factored form here:

https://brainly.com/question/43919