Q. 215 - Intermediate Algebra

Question

In the following exercises, factor completely.
$27q^2-3$

Step-by-Step Solution

Answer

The factored form of the given expression is $3(3q-1)(3q+1)$.

Step 1. Given information.

The given expression is:
$27q^2-3$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}27q^2-3& =& 3(9q^2-1)\\ & =& 3({\left(3q\right)}^2-1^2)\\ & =& 3(3q-1)(3q+1) [\because a^2-b^2=(a-b\left)\right(a+b\left)\right]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $3(3q-1)(3q+1)$.