1. **State the problem:** Simplify each expression and match it to one of the simplified forms: $10c$, $5c^2$, or $5c$. 2. **Expression 1:** $\frac{15bc}{3b}$ Use the rule $\frac{a \times b}{c \times b} = \frac{a}{c}$ when $b \neq 0$. Simplify: $$\frac{15bc}{3b} = \frac{\cancel{15}^5 \times b \times c}{\cancel{3}^1 \times b} = 5c$$ 3. **Expression 2:** $15bc \times \frac{2b}{3b^2}$ Rewrite multiplication: $$15bc \times \frac{2b}{3b^2} = \frac{15bc \times 2b}{3b^2} = \frac{30b^2 c}{3b^2}$$ Cancel $b^2$: $$\frac{30 \cancel{b^2} c}{3 \cancel{b^2}} = \frac{30c}{3} = 10c$$ 4. **Expression 3:** $15bc^2 \times \frac{2b}{6b^2}$ Rewrite multiplication: $$15bc^2 \times \frac{2b}{6b^2} = \frac{15bc^2 \times 2b}{6b^2} = \frac{30b^2 c^2}{6b^2}$$ Cancel $b^2$: $$\frac{30 \cancel{b^2} c^2}{6 \cancel{b^2}} = \frac{30c^2}{6} = 5c^2$$ **Final matches:** - $\frac{15bc}{3b} = 5c$ - $15bc \times \frac{2b}{3b^2} = 10c$ - $15bc^2 \times \frac{2b}{6b^2} = 5c^2$