This document provides the step-by-step solutions for simplifying four algebraic expressions by using the distributive property. Each expression contains two terms multiplied together where one term includes a variable and the other includes the variable squared or with an exponent. The solutions show expanding the expressions and combining like terms to obtain the simplified result for each problem.

1. Warm-up: Simplify. 1. (a+6)(a-3) 2. (3w+7)(2w +5) 3. (2y+3)(y 2 +3y-6) 4. (2b 2 -5b-3)(5b 2 +3b-2)

2. Answers 1. a 2 +3a-18 2. 6w 2 +29w+35 3. 2y 3 +9y 2 -3y-18 4. 10b 4 -19b 3 -34b 2 +b+6