1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.7 Simplifying and Evaluating Algebraic Expressions

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Identify like terms. o Simplify algebraic expressions by combining like terms. o Evaluate expressions for given values of the variables.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Notes If no number is written next to a variable, the coefficient is understood to be 1. If a negative sign (  ) is next to a variable, the coefficient is understood to be  1. For example, Identifying Like Terms

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Identifying Like Terms Like Terms Like terms (or similar terms) are terms that are constants or terms that contain the same variables raised to the same powers. Note: If there is more than one variable in a term, then the sum of the exponents on the variables is the degree of the term.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Like Terms From the following list of terms, pick out the like terms. Solution  7, 4.1, and 0 are like terms. (All are constants.) 2x,  x, and 5x are like terms.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Simplifying Algebraic Expression Combining Like Terms To combine like terms, add (or subtract) the coefficients and keep the common variable expression.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Combining Like Terms Combine like terms whenever possible. a.8x + 10x Solution b.6.5y − 2.3y Solution

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Combining Like Terms (cont.) Solution

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Combining Like Terms (cont.) Solution

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Combining Like Terms (cont.) Solution A fraction bar is a grouping symbol, similar to parentheses. So combine like terms in the numerator first.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Evaluating Algebraic Expressions To Evaluate an Algebraic Expression 1.Combine like terms, if possible. 2.Substitute the values given for any variables. 3.Follow the rules for order of operations.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Evaluating Algebraic Expressions a.Evaluate x 2 for x = 3 and for x =  4. Solution b.Evaluate –x 2 for x = 3 and for x =  4. Solution

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Simplifying and Evaluating Algebraic Expressions Simplify each expression below by combining like terms. Then evaluate the resulting expression using the given values for the variables. a.Simplify and evaluate 2x + 5 + 7x for x = −3. Solution Simplify first. Now evaluate.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Simplifying and Evaluating Algebraic Expressions (cont.) b.Simplify and evaluate 3ab − 4ab + 6a − a for a = 2, b = −1. Solution Simplify first. Now evaluate.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Simplifying and Evaluating Algebraic Expressions (cont.) c.Simplify and evaluate Solution Simplify first. Now evaluate.

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Simplifying the the following expressions by combining like terms. Simplify the expression. Then evaluate the resulting expression for x = 3 and y =  2.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Answers 1.  7x2.11y  16 3.9x  54.3b 2 5.6x  2y; 14