Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Real Numbers and Introduction to Algebra

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.7 Simplifying Expressions

Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Terms A term is a number or the product of a number and variables raised to powers. 7 5x 3 5 ‒ 4xy 2 ‒ 4 z 2 1 Terms Coefficient

Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Identify the numerical coefficient of each term. a. ‒ 6x The numerical coefficient is ‒ 6. b. 27z 3 The numerical coefficient is 27. c. ‒ y The numerical coefficient is ‒ 1. d. The numerical coefficient is

Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Like terms contain the same variables raised to the same powers. Terms that are not like terms are called unlike terms. Combining Like Terms To combine like terms, combine the numerical coefficients and multiply the result by the common variable factors. Like Terms

Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. a. 6x 2 + 7x 2 = 13x 2 b. 19xy – 30xy = ‒ 11xy c. 13xy 2 – 7x 2 y Can’t be combined (since the terms are not like terms) Simplify each expression by combining like terms. Example

Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. a. 4(5x + 7) = 4(5x) + 4(7) = 20x + 28 b. ‒ 3(x + 0.5y – 7) = ‒ 3(x) + 3(0.5y) – ( ‒ 3)(7) Find each product by using the distributive property to remove parentheses. Example = ‒ 3x + 1.5y + 21

Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. a. Twice a number, plus 9. 2x + 9 b. Seven times the sum of a number and two. Write each phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. Example 7 · (x + 2)= 7 · x + 7 · 2 = 7x + 14