1. 1-9 Simplifying Algebraic Expressions

2. Essential Question  What properties and conventions do I need to understand in order to simplify and evaluate algebraic expressions?

3. Definitions Term- a number or variable, or a product of numbers and variables that are separated by plus and minus signs Like Terms- terms with the same variable raised to the same power Coefficient- a number that is multiplied by a variable in an algebraic expression

4. Important Notes: Terms in an expression are separated by + and –. 7x + 5 – 3y 2 + y + x3x3 term A variable by itself, like y, has a coefficient of 1. So y = 1y. Coefficient Variable

5. Like Terms Unlike Terms 3x and 2x 5x 2 and 2x The exponents are different. 3.2 and n Only one term contains a variable 6a and 6b The variables are different w and w7w7 5 and 1.8 Important Notes:

6. Identify like terms in the list. Example 1 Look for like variables with like powers. 3t 5w 2 7t 9v 4w 2 8v Like terms: 3t and 7t 5w 2 and 4w 2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

7. Example 2 Identify like terms in the list. Look for like variables with like powers. Like terms: 2x and 8x 4y 3 and 5y 3 5z and 8z 2x 4y 3 8x 5z 5y 3 8z

8. x Combining like terms is like grouping similar objects. += x x x xx x xx xxxx x xxxx 4x4x+5x5x =9x9x To combine like terms that have variables, add or subtract the coefficients. Important Note:

9. Steps for Simplifying equations: 1.Identify like terms 2. Group the like terms in parentheses 3.Add the coefficients

10. Simplify. Example 3 A. 6t – 4t6t – 4t =2t2t B. 45x – 37y + 87 In this expression, there are no like terms to combine.

11. Example 4 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 5a 2 + b + 11b 2 – 6 (3a 2 + 2a 2 ) + (5b – 4b) + 11b 2 – 6 Simplify.

12. Example 5 4x 2 + 4y + 3x 2 – 4y + 2x 2 + 5 9x 2 + 5 4x 2 + 4y + 3x 2 – 4y + 2x 2 + 5 (4x 2 + 3x 2 + 2x 2 )+ (4y – 4y) + 5 Simplify.

13. Work Session  Textbook  Page 44  Questions 2-4; 8-16; 18-26 even only

14. (6a² - a²) + 16 5a² + 16 Like terms: 12a² and 4a² ; b and 5/6b; 4x³ and 3.5x³

15. Like terms: 2n and n/4; 6 and 7 Like terms: y³ and 5y³; 6³ and 6²

16. (5b + 7b) + 10 12b+ 10 (y + 3y) + 2x + 4 4y + 2x + 4 2d³ + (d + 3d) + 18 2d³ + 4d + 18

17. 8x4c² + 7c 6f ² + 2f 15p + 9q + 93a² + 3b + 2c

18. Homework  Workbook  page 9  All problems