1. **State the problem:** Expand and simplify the expression $$(c - 4)(c + 6) - (c + 2)(c - 3)$$. 2. **Recall the distributive property:** To expand products of binomials, use the FOIL method (First, Outer, Inner, Last). 3. **Expand each product:** - For $$(c - 4)(c + 6)$$: $$c \times c = c^2$$ $$c \times 6 = 6c$$ $$-4 \times c = -4c$$ $$-4 \times 6 = -24$$ So, $$(c - 4)(c + 6) = c^2 + 6c - 4c - 24 = c^2 + 2c - 24$$. - For $$(c + 2)(c - 3)$$: $$c \times c = c^2$$ $$c \times (-3) = -3c$$ $$2 \times c = 2c$$ $$2 \times (-3) = -6$$ So, $$(c + 2)(c - 3) = c^2 - 3c + 2c - 6 = c^2 - c - 6$$. 4. **Subtract the second expression from the first:** $$ (c^2 + 2c - 24) - (c^2 - c - 6) = c^2 + 2c - 24 - c^2 + c + 6 $$ 5. **Combine like terms:** - $$c^2 - c^2 = 0$$ - $$2c + c = 3c$$ - $$-24 + 6 = -18$$ 6. **Final simplified expression:** $$3c - 18$$ 7. **Factor if desired:** $$3(c - 6)$$ **Answer:** $$3(c - 6)$$