1. **State the problem:** Simplify each algebraic expression given. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$ This means multiply the term outside the parentheses by each term inside. 3. **Simplify each expression step-by-step:** **Problem 12:** $$-5(2y + 3)$$ Apply distributive property: $$-5 \times 2y + (-5) \times 3 = -10y - 15$$ This matches the given expression, so simplified form is: $$-10y - 15$$ **Problem 14:** $$7(5a - 9) - 4(8a - 7)$$ Distribute each: $$7 \times 5a - 7 \times 9 - 4 \times 8a + 4 \times 7 = 35a - 63 - 32a + 28$$ Combine like terms: $$35a - 32a + (-63 + 28) = (35a - 32a) + (-63 + 28) = 3a - 35$$ **Problem 16:** $$5r - 6(r - 2s) + 18r$$ Distribute: $$5r - 6r + 12s + 18r$$ Combine like terms: $$5r - 6r + 18r + 12s = (5r - 6r + 18r) + 12s = 17r + 12s$$ **Problem 18:** $$( -28 + 17v ) - ( 2v - 19 )$$ Distribute the minus sign: $$-28 + 17v - 2v + 19$$ Combine like terms: $$(-28 + 19) + (17v - 2v) = -9 + 15v$$ 4. **Final simplified expressions:** - Problem 12: $$-10y - 15$$ - Problem 14: $$3a - 35$$ - Problem 16: $$17r + 12s$$ - Problem 18: $$15v - 9$$