2 Chapter Chapter 2 Equations, Inequalities and Problem Solving

Simplifying Algebraic Expressions Section 2.1 Simplifying Algebraic Expressions

Identifying Terms, Like Terms, and Unlike Terms Objective 1 Identifying Terms, Like Terms, and Unlike Terms

Terms A term is a number or the product of a number and variables raised to powers. The numerical coefficient of a term is the numerical factor. The numerical coefficient of 3x is 3. Terms Coefficient 7 7 5x3 5 ‒4xy2 ‒4 z2 1

Example Identify the numerical coefficient of each term. a. ‒6x b. 27z3 c. ‒ y d. The numerical coefficient is ‒6. The numerical coefficient is 27. The numerical coefficient is ‒1. The numerical coefficient is

Like Terms Like terms contain the same variables raised to the same powers. Terms that are not like terms are called unlike terms. Like Terms Unlike Terms 3x, 2x 5x, 5x2

Example Determine whether the terms are like or unlike. a. b. c. d.

Objective 2 Combining Like Terms

Like Terms Simplifying the sum or difference of like terms is called combining like terms.

Example Simplify each expression by combining like terms. a. 6x2 + 7x2 b. 19xy – 30xy c. 13xy2 – 7x2y = 13x2 = ‒11xy Can’t be combined (since the terms are not like terms)

Combining Like Terms To combine like terms, combine the numerical coefficients and multiply the result by the common variable factors.

Example Simplify each expression by combining like terms. a. 7y + 2y + 6 + 10 = (7 + 2)y + (6 + 10) = 9y + 16 b. 0 – 2x + 4 + x – 11 = (–2 + 1)x + (4 – 11) = –x – 7

Using the Distributive Property Objective 3 Using the Distributive Property

Example Find each product by using the distributive property to remove parentheses. a. 4(5x + 7) b. ‒3(x + 0.5y – 7) = 4(5x) + 4(7) = 20x + 28 = ‒3(x) + 3(0.5y) – (‒3)(7) = ‒3x + 1.5y + 21

Example Simplify each expression. a. 4(4x – 6) + 20 = 16x – 24 + 20 b. 5 – (3x + 9) + 6x = 5 – 3x – 9 + 6x = 3x – 4

Example Simplify each expression. c. –3(7x + 1) – (4x – 2) d. 8 + 11(2y – 9) = 8 + 22y – 99 = 22y – 91

Writing Word Phrases as Algebraic Expressions Objective 4 Writing Word Phrases as Algebraic Expressions

Example Write each phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. a. Twice a number, plus 9. 2x + 9 b. Seven times the sum of a number and two. 7 · (x + 2) = 7 · x + 7 · 2 = 7x + 14

Example Write each phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. c. Three times the sum of a number and 6 3(x + 6) = 3x + 18 d. The sum of a number and 2, divided by 5