1. Objective The student will be able to: Combine like terms to simplify expressions. Use the distributive property to simplify expressions. Simplify expressions using distributive property and like terms together in the same problem. Designed by Skip Tyler, Varina High School and Nicole Kessinger, Deep Run High School – edited by Gloria Kent, South Lenoir High School, Nov., 2009.

2. The Distributive Property The process of using the number on the outside of the parentheses with each term on the inside of the parentheses. a(b + c) = ab + ac and(b + c) a = ba + ca a(b - c) = ab - acand(b - c) a = ba - ca Example #1 5(x + 7) 5 x + 5 7 5x + 35

3. Example #2 3(m - 4) 3 m - 3 4 3m - 12 Example #3 -2(y + 3) -2 y + (-2) 3 -2y + (-6) -2y - 6

4. Which statement demonstrates the distributive property incorrectly? 1.3(x + y + z) = 3x + 3y + 3z 2.(a + b) c = ac + bc 3.6(3k - 4) = 18k - 24 4.5(2 + 3x) = 10 + 3x Answer Now

5. A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x ³

6. The coefficient is the number attached and in front of the variable. Examples 1) 4a 4 2) y 2 1 3)

7. Like Terms are terms with the same variable AND with the same exponent. To simplify expressions with like terms, simply combine the like terms by adding the coefficients.

8. Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x 3 y, xy 3 No, the exponents are on different variables.

9. Which of the following is the simplified form of -4x + 7x ? 1.-4 2.3x 3.-3x 4.4 Answer Now

10. The above expression simplifies to: 5a and a are like terms and are like terms

11. 12a 2) 6.1y - 3.2y 2.9y 3) 4x 2 y + x 2 y 5x 2 y 4) 3m 2 n + 10mn 2 + 7m 2 n - 4mn 2 10m 2 n + 6mn 2 Simplify 1) 5a + 7a

12. 21a + 6b 6) 4d + 6a 2 - d + 12a 2 18a 2 + 3d 7) y 5) 13a + 8a + 6b

13. Which of the following is the simplified form of 5x - 4 - 7x + 14 ? Answer Now 1.-12x + 10 2.-2x + 10 3.2x - 18 4.12x – 18

14. If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle? Answer Now 1.4x - 2 2.4x + 2 3.5x - 2 4.5x - 7

15. Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? Answer Now 1.-36 2.3a - 36 3.8a - 36 4.8a + 36