1. **Problem:** Simplify $-5(2x + 1) + 2(3x - 2y)$. 2. **Formula and rules:** Use the distributive property $a(b + c) = ab + ac$ to remove parentheses. 3. **Step-by-step:** - Distribute: $-5 \times 2x = -10x$, $-5 \times 1 = -5$, $2 \times 3x = 6x$, $2 \times (-2y) = -4y$ - Write expression: $-10x - 5 + 6x - 4y$ - Combine like terms: $(-10x + 6x) = -4x$ - Final simplified expression: $$\boxed{-4x - 5 - 4y}$$ 2. **Problem:** Simplify $4(-9x - 2) - 3(4x + 8)$. 3. **Step-by-step:** - Distribute: $4 \times (-9x) = -36x$, $4 \times (-2) = -8$, $-3 \times 4x = -12x$, $-3 \times 8 = -24$ - Write expression: $-36x - 8 - 12x - 24$ - Combine like terms: $(-36x - 12x) = -48x$, $(-8 - 24) = -32$ - Final simplified expression: $$\boxed{-48x - 32}$$ 3. **Problem:** Simplify $-2(6x + 5) - 2(2y - 9)$. 3. **Step-by-step:** - Distribute: $-2 \times 6x = -12x$, $-2 \times 5 = -10$, $-2 \times 2y = -4y$, $-2 \times (-9) = +18$ - Write expression: $-12x - 10 - 4y + 18$ - Combine like terms: $(-10 + 18) = 8$ - Final simplified expression: $$\boxed{-12x + 8 - 4y}$$