1. Chapter 1 Section 8 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Simplifying Expressions 1 1 4 4 3 3 2 2 5 5 1.81.8 Simplify expressions. Identify terms and numerical coefficients. Identify like terms. Combine like terms. Simplify expressions from word phrases.

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Slide 1.8- 3 Simplify expressions.

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Simplify each expression. Solution: Simplifying Expressions Slide 1.8- 4

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Identify terms and numerical coefficients. Slide 1.8- 5

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Identify terms and numerical coefficients. A term is a number, a variable, or a product or quotient of numbers and variables raised to powers, such as,,,,, and. Terms In the term 9x, the numerical coefficient, or simply coefficient, of the variable x is 9. In the term −8m 2 n the numerical coefficient of m 2 n is −8. It is important to be able to distinguish between terms and factors. For example, in the expression, there are two terms, and. Terms are separated by a + or − sign. On the other hand, in the one-term expression, and are factors. Slide 1.8- 6

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Identify like terms. Slide 1.8- 7

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Identify like terms. Terms with exactly the same variables that have the same exponents are like terms. For example, 9m and 4m have the same variable and are like terms. The terms −4y and 4y 2 have different exponents and are unlike terms. andandLike terms andandUnlike terms Slide 1.8- 8

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4 Objective 4 Combine like terms. Slide 1.8- 9

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Recall the distributive property: Combine like terms. This form of the distributive property may be used to find the sum or difference of like terms. Using the distributive property in this way is called combining like terms. This statement can also be written “backward” as. Slide 1.8- 10

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Combine like terms in each expression. Solution: Combining Like Terms Cannot be combined Slide 1.8- 11

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Simplify each expression. Solution: Simplifying Expressions Involving Like Terms Constants are like terms and may be combined. Slide 1.8- 12

13. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5 Objective 5 Simplify expressions from word phrases. Slide 1.8- 13

14. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Translate to a mathematical expression and simplify. Three times a number, subtracted from the sum of the number and 8. Solution: Translating Words to a Mathematical Expression Remember, we are dealing with an expression to be simplified, not an equation to be solved. Slide 1.8- 14