1. **Problem:** Simplify and factor the expression $4(7x + 6) - 3(6x - 7)$. Step 1: Distribute the constants: $$4 \times 7x + 4 \times 6 - 3 \times 6x + 3 \times 7 = 28x + 24 - 18x + 21$$ Step 2: Combine like terms: $$28x - 18x + 24 + 21 = 10x + 45$$ Step 3: Factor the simplified expression: $$10x + 45 = 5(2x + 9)$$ 2. **Problem:** Simplify and factor the expression $9(4x + 8) + 2(6x - 8)$. Step 1: Distribute the constants: $$9 \times 4x + 9 \times 8 + 2 \times 6x - 2 \times 8 = 36x + 72 + 12x - 16$$ Step 2: Combine like terms: $$36x + 12x + 72 - 16 = 48x + 56$$ Step 3: Factor the simplified expression: $$48x + 56 = 8(6x + 7)$$ 3. **Problem:** Simplify and factor the expression $-2(1 - 8x) - (x + 4)$. Step 1: Distribute the constants: $$-2 \times 1 + -2 \times (-8x) - x - 4 = -2 + 16x - x - 4$$ Step 2: Combine like terms: $$16x - x - 2 - 4 = 15x - 6$$ Step 3: Factor the simplified expression: $$15x - 6 = 3(5x - 2)$$ 4. **Problem:** Simplify and factor the expression $3(8x - 3) - 2(3x + 9)$. Step 1: Distribute the constants: $$3 \times 8x - 3 \times 3 - 2 \times 3x - 2 \times 9 = 24x - 9 - 6x - 18$$ Step 2: Combine like terms: $$24x - 6x - 9 - 18 = 18x - 27$$ Step 3: Factor the simplified expression: $$18x - 27 = 9(2x - 3)$$ 5. **Problem:** Simplify and factor the expression $6(5x + 3) - 2(3 - x)$. Step 1: Distribute the constants: $$6 \times 5x + 6 \times 3 - 2 \times 3 + 2 \times x = 30x + 18 - 6 + 2x$$ Step 2: Combine like terms: $$30x + 2x + 18 - 6 = 32x + 12$$ Step 3: Factor the simplified expression: $$32x + 12 = 4(8x + 3)$$ 6. **Problem:** Simplify and factor the expression $10(2x - 1) + 3(5x - 6)$. Step 1: Distribute the constants: $$10 \times 2x - 10 \times 1 + 3 \times 5x - 3 \times 6 = 20x - 10 + 15x - 18$$ Step 2: Combine like terms: $$20x + 15x - 10 - 18 = 35x - 28$$ Step 3: Factor the simplified expression: $$35x - 28 = 7(5x - 4)$$ 7. **Problem:** Simplify and factor the expression $-4(x - 3) + 2(6x + 1)$. Step 1: Distribute the constants: $$-4 \times x + 4 \times 3 + 2 \times 6x + 2 \times 1 = -4x + 12 + 12x + 2$$ Step 2: Combine like terms: $$-4x + 12x + 12 + 2 = 8x + 14$$ Step 3: Factor the simplified expression: $$8x + 14 = 2(4x + 7)$$ 8. **Problem:** Simplify and factor the expression $-8(6 - 3x) - 6(x - 3)$. Step 1: Distribute the constants: $$-8 \times 6 + 8 \times 3x - 6 \times x + 6 \times 3 = -48 + 24x - 6x + 18$$ Step 2: Combine like terms: $$24x - 6x - 48 + 18 = 18x - 30$$ Step 3: Factor the simplified expression: $$18x - 30 = 6(3x - 5)$$