Q. 222 - Intermediate Algebra

Question

In the following exercises, factor completely.

$27u^3+1000$

Step-by-Step Solution

Answer

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

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,

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