Q. 200 - Intermediate Algebra

Question

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$125-27w^3$

Step-by-Step Solution

Answer

The factored form of the given expression is $(5-3w)(25+15w+9w^2)$.

Step 1. Given information.

The given expression is:

$125-27w^3$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}125-27w^3& =& 5^3-{\left(3w\right)}^3\\ & =& (5-3w)\left(5^2+\left(5\right)\left(3w\right)+{\left(3w\right)}^2\right) \left[\because a^3-b^3=(a-b)(a^2+ab+b^2)\right]\\ & =& (5-3w)\left(25+15w+9w^2\right)\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(5-3w)(25+15w+9w^2)$.