Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$m^2-6m+9-16n^2$

Short answer

The factored form of the given expression is$(m-3-4n)(m-3+4n)$.

Step-by-step solution

Step 1. Given information.

The given expression is:
$m^2-6m+9-16n^2$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}{m}^2-6m+9-16n^2& =& (m^2-2(m\left)\right(3)+3^2)-4^2{n}^2\\ & =& {(m-3)}^2-{\left(4n\right)}^2\left[\because {(a-b)}^2=a^2-2ab+b^2\right]\\ & =& (m-3-4n)(m-3+4n)\left[\because {a^2-b}^2=(a-b)(a+b)\right]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is$(m-3-4n)(m-3+4n)$.