Q. 213 - Intermediate Algebra

Question

In the following exercises, factor completely.
$64a^2-25$

Step-by-Step Solution

Answer

The factored form of the given expression is $(8a-5)(8a+5)$.

Step 1. Given information.

The given expression is:
$64a^2-25$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}64a^2-25& =& 8^2{a}^2-5^2\\ & =& {\left(8a\right)}^2-5^2\\ & =& (8a-5)(8a+5) [\because a^2-b^2=(a-b\left)\right(a+b\left)\right]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(8a-5)(8a+5)$.