1. Stating the problem: Simplify and factor the expressions $(x+6)^2$ and $x^2 - 36$. 2. Expand and simplify $(x+6)^2$: $$ (x+6)^2 = (x+6)(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36 $$ 3. Factor $x^2 - 36$ using the difference of squares: $$ x^2 - 36 = (x - 6)(x + 6) $$ Final answers: - $(x+6)^2 = x^2 + 12x + 36$ - $x^2 - 36 = (x - 6)(x + 6)$