1. **Problem c:** Simplify $-4(p - 3)^2 + 2(2p - 6)$. 2. Use the formula for squaring a binomial: $ (a - b)^2 = a^2 - 2ab + b^2 $. 3. Expand $ (p - 3)^2 = p^2 - 2 \times p \times 3 + 3^2 = p^2 - 6p + 9 $. 4. Multiply by $-4$: $-4(p^2 - 6p + 9) = -4p^2 + 24p - 36$. 5. Expand $2(2p - 6) = 4p - 12$. 6. Add the two expressions: $-4p^2 + 24p - 36 + 4p - 12 = -4p^2 + (24p + 4p) + (-36 - 12) = -4p^2 + 28p - 48$. --- 1. **Problem d:** Simplify $\frac{2}{3}(12x^2 + 6x)$. 2. Distribute $\frac{2}{3}$: $\frac{2}{3} \times 12x^2 + \frac{2}{3} \times 6x$. 3. Calculate each term: $\frac{2}{3} \times 12x^2 = \cancel{\frac{2}{3}} \times \cancel{12}x^2 = 8x^2$, $\frac{2}{3} \times 6x = \cancel{\frac{2}{3}} \times \cancel{6}x = 4x$. 4. Final expression: $8x^2 + 4x$. --- 1. **Problem f:** Simplify $-\frac{3}{2} y + 3^2 \left( \frac{2}{3} y - 1 \right)^2$. 2. Calculate $3^2 = 9$. 3. Expand $\left( \frac{2}{3} y - 1 \right)^2$ using $ (a - b)^2 = a^2 - 2ab + b^2 $: $$\left( \frac{2}{3} y \right)^2 - 2 \times \frac{2}{3} y \times 1 + 1^2 = \frac{4}{9} y^2 - \frac{4}{3} y + 1$$ 4. Multiply by 9: $$9 \times \left( \frac{4}{9} y^2 - \frac{4}{3} y + 1 \right) = 9 \times \frac{4}{9} y^2 - 9 \times \frac{4}{3} y + 9 \times 1 = 4 y^2 - 12 y + 9$$ 5. Add $-\frac{3}{2} y$: $$-\frac{3}{2} y + 4 y^2 - 12 y + 9 = 4 y^2 - \left( 12 y + \frac{3}{2} y \right) + 9 = 4 y^2 - \frac{24}{2} y - \frac{3}{2} y + 9 = 4 y^2 - \frac{27}{2} y + 9$$ 6. Final simplified expression: $4 y^2 - \frac{27}{2} y + 9$.