2.7 Multiplying and Dividing Expressions

1. 2.7 Multiplying and Dividing Expressions • Objectives: Multiply expressions containing variables. Divide expressions containing variables. • Standards Addressed: 2.1.8.E: Simplify and expand algebraic expressions using exponential forms. 2.2.8.A: Complete calculations by applying the order of operations.

2. When solving equations, you often need to multiply and divide not only single numbers, but also larger expressions that may include variables.

3. Exponents

4. Ex. 1

5. Ex. 1 Simplify. • C. • D. 3x2 -24x -35x + 7x2

6. Ex. 2

7. Ex. 2b. (2b – 5c) -4(3b + c) • (2b – 5c) + (-12b – 4c) • -10b – 9c

9. Ex. 3A

10. Ex. 3b -2m2 – 3

11. Ex. 3c • -2x + 1

12. Ex. 3d -14x + 6y

13. Ex. 4 George is in charge of supplies for a mountain-climbing guide company. He is trying to locate carabiners for four climbing teams. George’s preferred brand of carabiners are available at 3 outfitters as follows: Outfitter A has 4 boxes plus 6 loose carabiners. Outfitter B has 6 boxes, but one box is missing 3 carabiners. Outfitter C has 10 boxes plus 5 loose carabiners. Assuming each box contains an equal number of carabiners, write an expression describing the total number of carabiners available. Write another expression describing the number of carabiners available for each team if the carabiners are divided equally among the teams. A: 4c + 6 B: 6c – 3 C: 10c + 5 4c + 6 6c – 3 + 10c + 5 = (20c + 8) ÷ 4 = 5c +2