1. **State the problem:** Simplify the algebraic expressions given: - $20m + 500$ - $10(m + 20) + 10(m + 30)$ - $10m + 50m$ - $10m + 200 + 10m + 300$ 2. **Use distributive property and combine like terms:** For the second expression: $$10(m + 20) + 10(m + 30) = 10m + 200 + 10m + 300$$ 3. **Simplify each expression step-by-step:** - First expression: $20m + 500$ (already simplified) - Second expression: $10m + 200 + 10m + 300$ Combine like terms: $$10m + 10m = 20m$$ $$200 + 300 = 500$$ So, second expression simplifies to: $$20m + 500$$ - Third expression: $10m + 50m$ Combine like terms: $$10m + 50m = 60m$$ - Fourth expression: $10m + 200 + 10m + 300$ Combine like terms: $$10m + 10m = 20m$$ $$200 + 300 = 500$$ So, fourth expression simplifies to: $$20m + 500$$ 4. **Summary:** - $20m + 500$ (first expression) - $20m + 500$ (second expression simplified) - $60m$ (third expression simplified) - $20m + 500$ (fourth expression simplified) All simplifications are done by combining like terms and applying distributive property where needed. **Final answers:** - $20m + 500$ - $20m + 500$ - $60m$ - $20m + 500$