a) \( 8 y-16 y^{2} \) \( 4 y^{2} \) b) \( 9-4 a^{2} \) \( 4 a^{2}-16 a+15 \) c) \( 6 x^{2}+x y-15 y^{2} \) \( 6 x^{2}+10 x y \) d) \( x^{2}+2 x^{2}-4 x-8 \) \( 6 x^{2}-5 x-14 \)

Let's solve each part step by step, simplifying the expressions provided. ### Part a We have the expressions: 1. \( 8y - 16y^2 \) 2. \( 4y^2 \) **Step 1: Combine the expressions.** To combine these, we can rewrite the first expression: \[ 8y - 16y^2 = 8y - 4y^2 \cdot 4 \] Now, we can combine them: \[ 8y - 16y^2 - 4y^2 = 8y - 20y^2 \] ### Part b We have the expressions: 1. \( 9 - 4a^2 \) 2. \( 4a^2 - 16a + 15 \) **Step 1: Combine the expressions.** To combine these, we can rewrite the first expression: \[ 9 - 4a^2 - (4a^2 - 16a + 15) = 9 - 4a^2 - 4a^2 + 16a - 15 \] Now, simplify: \[ = 16a - 8a^2 - 6 \] ### Part c We have the expressions: 1. \( 6x^2 + xy - 15y^2 \) 2. \( 6x^2 + 10xy \) **Step 1: Combine the expressions.** To combine these, we can rewrite the first expression: \[ 6x^2 + xy - 15y^2 + 6x^2 + 10xy = 12x^2 + 11xy - 15y^2 \] ### Part d We have the expressions: 1. \( x^2 + 2x^2 - 4x - 8 \) 2. \( 6x^2 - 5x - 14 \) **Step 1: Combine the expressions.** To combine these, we can rewrite the first expression: \[ x^2 + 2x^2 - 4x - 8 = 3x^2 - 4x - 8 \] Now, combine with the second expression: \[ 3x^2 - 4x - 8 + 6x^2 - 5x - 14 = 9x^2 - 9x - 22 \] ### Summary of Results - **Part a:** \( 8y - 20y^2 \) - **Part b:** \( 16a - 8a^2 - 6 \) - **Part c:** \( 12x^2 + 11xy - 15y^2 \) - **Part d:** \( 9x^2 - 9x - 22 \)