Question

In the following exercises, factors completely:

$c^3-1000d^3$.

Short answer

The factors for the expression is,$(c-10d)(c^2+10cd+100d^2)$.

Step-by-step solution

Step 1. Given Information.

The expression is,

$c^3-1000d^3$.

Step 2. Factor completely.

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

$c^3-1000d^3={\left(c\right)}^3-{\left(10d\right)}^3$

role="math" localid="1647718105719" $$\begin{gathered} =(c-d)({\left(c\right)}^2+(c\times 10d)+{\left(10d\right)}^2) \\ =(c-d)(c^2+10cd+100d^2) \end{gathered}$$