1. **State the problem:** Simplify the algebraic expression $5w^2 + 3w + 2w^2 - 2w$. 2. **Group like terms:** Combine terms with $w^2$ and terms with $w$ separately. 3. **Add coefficients of like terms:** $$5w^2 + 2w^2 = (\cancel{5} + \cancel{2})w^2 = 7w^2$$ $$3w - 2w = (\cancel{3} - \cancel{2})w = 1w = w$$ 4. **Write the simplified expression:** $$7w^2 + w$$ 5. **Explain:** We combined the coefficients of the same powers of $w$ by adding or subtracting them, which is the basic rule for simplifying algebraic expressions. **Final answer:** $7w^2 + w$