1. **State the problem:** Use the distributive property to simplify and find the product for the expressions given. 2. **Recall the distributive property formula:** $$a \times (b + c) = a \times b + a \times c$$ This means you multiply the factor outside the parentheses by each term inside the parentheses separately, then add the results. 3. **Solve each part:** **a.** $2 \times (4 + 7)$ $$= 2 \times 4 + 2 \times 7$$ $$= 8 + 14$$ $$= 22$$ **b.** $4 \times (5 + 8)$ $$= 4 \times 5 + 4 \times 8$$ $$= 20 + 32$$ $$= 52$$ **c.** $3 \times (10 + 9)$ $$= 3 \times 10 + 3 \times 9$$ $$= 30 + 27$$ $$= 57$$ **d.** $6 \times (13 + 20)$ $$= 6 \times 13 + 6 \times 20$$ $$= 78 + 120$$ $$= 198$$ 4. **Decompose one factor and use distributive property:** **e.** $5 \times 17$ Decompose 17 as $10 + 7$ $$= 5 \times (10 + 7)$$ $$= 5 \times 10 + 5 \times 7$$ $$= 50 + 35$$ $$= 85$$ **f.** $9 \times 18$ Decompose 18 as $10 + 8$ $$= 9 \times (10 + 8)$$ $$= 9 \times 10 + 9 \times 8$$ $$= 90 + 72$$ $$= 162$$