1. **State the problem:** Multiply the polynomials $ (v - 5)(v + 4) $ and simplify the result. 2. **Recall the formula:** To multiply two binomials, use the distributive property (also known as FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** Here, $a = v$, $b = -5$, $c = v$, and $d = 4$. Calculate each term: - $ac = v \times v = v^2$ - $ad = v \times 4 = 4v$ - $bc = -5 \times v = -5v$ - $bd = -5 \times 4 = -20$ 4. **Combine all terms:** $$ v^2 + 4v - 5v - 20 $$ 5. **Simplify like terms:** $$ v^2 + \cancel{4v} - \cancel{5v} - 20 = v^2 - v - 20 $$ **Final answer:** $$ v^2 - v - 20 $$