Q. 214 - Intermediate Algebra

Question

In the following exercises, factor completely.
$121x^2-144$

Step-by-Step Solution

Answer

The factored form of the given expression is $(11x-12)(11x+12)$.

Step 1. Given information.

The given expression is:

$121x^2-144$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}121x^2-144& =& {\left(11\right)}^2{x}^2-{\left(12\right)}^2 \\ & =& {\left(11x\right)}^2-{\left(12\right)}^2\\ & =& (11x-12)(11x+12) [\because a^2-b^2=(a-b\left)\right(a+b\left)\right]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(11x-12)(11x+12)$.