Question

In the following exercises, factor completely.

$27u^3+1000$

Short answer

The simplified expression is$(3u+10)(9u^2-30u+100)$

Step-by-step solution

Step 1. Given Information 

The given expression is$27u^3+1000$

Step 2. Calculation

As we know the identity,

$a^3+b^3=(a+b)(a^2-ab+b^2)$where a and b are real numbers.

Now, we will use the identity to simplify the expression,

role="math" localid="1644566594473" $$\begin{gathered} 27u^3+1000={\left(3u\right)}^3+{\left(10\right)}^3 \\ =(3u+10)({\left(3u\right)}^2-3u\times 10+{\left(10\right)}^2) \\ =(3u+10)(9u^2-30u+100) \end{gathered}$$