Q. 217 - Intermediate Algebra

Question

In the following exercises, factor completely.
$16x^2-72x+81$

Step-by-Step Solution

Answer

The factored form of the given expression is ${(4x-9)}^2$.

Step 1. Given information.

The given expression is:
$16x^2-72x+81$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}16x^2-72x+81& =& {\left(4x\right)}^2-2\left(4x\right)\left(9\right)+9^2\\ & =& {(4x-9)}^2 [\because (a-b{)}^2=a^2-2ab+b^2]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is ${(4x-9)}^2$.