Step 1: Recognize the expression as a difference of squares. The expression $(x+4)^2 - 9^2$ is in the form $a^2 - b^2$, where $a = (x+4)$ and $b = 9$. Step 2: Apply the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$. Substitute $a=(x+4)$ and $b=9$ into the formula: $$ (x+4)^2 - 9^2 = ((x+4) - 9)((x+4) + 9) $$ Step 3: Simplify the terms within each parenthesis. For the first parenthesis: $$ (x+4) - 9 = x + 4 - 9 = x - 5 $$ For the second parenthesis: $$ (x+4) + 9 = x + 4 + 9 = x + 13 $$ Step 4: Write the completely factorized expression. $$ (x+4)^2 - 9^2 = (x-5)(x+13) $$ $$\boxed{(x-5)(x+13)}$$ Last free one today — make it count tomorrow, or type /upgrade for unlimited.