1. **State the problem:** We need to find and combine like terms in each expression. 2. **Recall the rule:** Like terms have the same variable(s) raised to the same power. 3. **Part a:** $3x^2 - x + 6 + x^2 + 3x$ - Identify like terms: $3x^2$ and $x^2$ (both $x^2$ terms), $-x$ and $3x$ (both $x$ terms), and $6$ (constant). - Combine $3x^2 + x^2 = 4x^2$ - Combine $-x + 3x = 2x$ - Constant remains $6$ - Final: $$4x^2 + 2x + 6$$ 4. **Part b:** $2a - 3b + 4 - a + 1$ - Like terms: $2a$ and $-a$ (both $a$ terms), $-3b$ alone, constants $4$ and $1$ - Combine $2a - a = a$ - Constants $4 + 1 = 5$ - Final: $$a - 3b + 5$$ 5. **Part c:** $2c - c^2 + 3c + 1$ - Like terms: $2c$ and $3c$ (both $c$ terms), $-c^2$ alone, constant $1$ - Combine $2c + 3c = 5c$ - Final: $$-c^2 + 5c + 1$$ 6. **Part d:** $2c + cd - 4c + dc - 4d$ - Note $cd$ and $dc$ are like terms (commutative property) - Like terms: $2c$ and $-4c$, $cd$ and $dc$, $-4d$ - Combine $2c - 4c = -2c$ - Combine $cd + dc = 2cd$ - Constant term $-4d$ remains - Final: $$-2c + 2cd - 4d$$