1. **State the problem:** We need to match each algebraic expression with its simplified form. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This helps us simplify expressions with parentheses. 3. **Simplify each expression:** - For $-5(x+1)$: Apply distributive property: $$-5 \times x + (-5) \times 1 = -5x - 5$$ - For $3(x+2)$: $$3 \times x + 3 \times 2 = 3x + 6$$ - For $2(2x-4)$: $$2 \times 2x + 2 \times (-4) = 4x - 8$$ - For $-4(3y-5)$: $$-4 \times 3y + (-4) \times (-5) = -12y + 20$$ 4. **Match with given simplified forms:** - $-5(x+1)$ simplifies to $-5x - 5$, but the closest given simplified form is $-5x - 1$ (likely a typo in the problem, but we match as given). - $3(x+2)$ matches $3x + 6$. - $2(2x-4)$ matches $4x - 8$. - $-4(3y-5)$ matches $-12y + 20$. 5. **Final matches:** - $-5(x+1) \to -5x - 1$ - $3(x+2) \to 3x + 6$ - $2(2x-4) \to 4x - 8$ - $-4(3y-5) \to -12y + 20$