HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.1 Simplifying and Evaluating Algebraic Expressions

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

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

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Simplifying Algebraic Expressions Like Terms Like terms (or similar terms) are terms that are constants or terms that contain the same variables raised to the same exponents. Note: The sum of the exponents on the variables is the degree of the term.

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.

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

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 8x + 10x b.6.5y − 2.3y Solution 6.5y – 2.3y = (8 + 10)x= 18x By the distributive property = (6.5 – 2.3)y= 4.2y By the distributive property

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 Use the commutative property of addition.

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 Simplify by using the distributive property twice. Use the commutative property of addition. By the distributive property Combine like terms.

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. Combine like terms. Reduce the fraction.

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. (See Section 1.8.)

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

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 x for x = −3. Solution Simplify first. Now evaluate. 2x x= 2x + 7x + 5 = 9x + 5 9x + 5= 9(−3) + 5= − = −22

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. 3ab − 4ab + 6a − a Now evaluate. −ab + 5a = −ab + 5a = −1(2)(−1) + 5(2) Note: −ab = −1ab = = 12

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.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Simplify the following expressions by combining like terms. 1. −2x − 5x 2. 12y + 6 − y (x − 1) + 4x 4. Simplify the expression. Then evaluate the resulting expression for x = 3 and y = − (x + 3y) + 4(x – y)

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.  7x 2. 11y x  x + 2y; 14