1. The problem is to simplify and solve the expression $(r - 7)(r + 6)$ for given values of $r$. 2. The formula used is the distributive property (FOIL method) for multiplying binomials: $$ (a - b)(a + c) = a^2 + ac - ab - bc $$ 3. Applying this to $(r - 7)(r + 6)$: $$ (r - 7)(r + 6) = r^2 + 6r - 7r - 42 $$ 4. Simplify the middle terms: $$ r^2 - r - 42 $$ 5. Now, substitute the given values of $r$: - For $r = 7$: $$ 7^2 - 7 - 42 = 49 - 7 - 42 = 0 $$ - For $r = -6$: $$ (-6)^2 - (-6) - 42 = 36 + 6 - 42 = 0 $$ 6. Both values satisfy the expression, confirming the roots $r = 7$ and $r = -6$. Final answer: The expression simplifies to $$r^2 - r - 42$$ and the roots are $$r = 7$$ and $$r = -6$$.