1. **State the problem:** Multiply and simplify the expression $$\frac{p^2 - 4}{15p} \times \frac{3}{2 - p}$$ to its lowest terms. 2. **Recall formulas and rules:** - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - When multiplying fractions, multiply numerators together and denominators together. - Simplify by factoring and canceling common factors. 3. **Factor the numerator $$p^2 - 4$$:** $$p^2 - 4 = (p - 2)(p + 2)$$ 4. **Rewrite the expression with factored form:** $$\frac{(p - 2)(p + 2)}{15p} \times \frac{3}{2 - p}$$ 5. **Notice that $$2 - p = -(p - 2)$$, so rewrite denominator:** $$\frac{(p - 2)(p + 2)}{15p} \times \frac{3}{-(p - 2)} = \frac{(p - 2)(p + 2)}{15p} \times \frac{3}{-1 \times (p - 2)}$$ 6. **Multiply numerators and denominators:** $$\frac{(p - 2)(p + 2) \times 3}{15p \times -1 \times (p - 2)}$$ 7. **Cancel common factor $$(p - 2)$$:** $$\frac{\cancel{(p - 2)}(p + 2) \times 3}{15p \times -1 \times \cancel{(p - 2)}} = \frac{3(p + 2)}{-15p}$$ 8. **Simplify the fraction:** $$\frac{3(p + 2)}{-15p} = \frac{\cancel{3}(p + 2)}{-\cancel{15}5p} = \frac{p + 2}{-5p} = -\frac{p + 2}{5p}$$ **Final answer:** $$-\frac{p + 2}{5p}$$