Question

Use a Special Factoring Formula to factor the expression

${\left(x+3\right)}^2-4$

Short answer

The solution${\left(x+3\right)}^2-4=\left(x+1\right)\left(x+5\right)$

Step-by-step solution

Step 1. Apply the Factoring Formula.

If A and B are any real numbers or algebraic expressions, then

$A^2-B^2=\left(A+B\right)\left(A-B\right)$

Step 2. Analyze the given expression.

Given${\left(x+3\right)}^2-4$

Here

$\begin{array}{l}{A}^2={\left(x+3\right)}^2,B^2=4\\ \Rightarrow A=x+3,B=2\end{array}$

Step 3. Solve the expression.

Substitute the values in the Factoring formula to get:

$\begin{array}{l}{\left(x+3\right)}^2-4={\left(x+3\right)}^2-2^2\\ \Rightarrow {\left(x+3\right)}^2-4=\left(x+3-2\right)\left(x+3+2\right)\\ \Rightarrow {\left(x+3\right)}^2-4=\left(x+1\right)\left(x+5\right)\end{array}$