Q. 221 - Intermediate Algebra

Question

In the following exercises, factor completely.

$125-8y^3$

Step-by-Step Solution

Answer

The simplified expression is $\left(5-2y\right)\left(25+10y+4y^2\right)$

Step 1. Given Information

The given expression is $125-8y^3$

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,

$$\begin{gathered} 125-8y^3={\left(5\right)}^3-{\left(2y\right)}^3 \\ =(5-2y)(5^2+5\times 2y+{\left(2y\right)}^2) \\ =(5-2y)(25+10y+4y^2) \end{gathered}$$