1. Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simplifying, Adding, and Subtracting Polynomials. 3.3 1. Simplifying polynomials in one variable by combining like terms 2. Add polynomials in one variable. 3. Write an expression for the perimeter of a given shape. 4. Subtract polynomials in one variable.

2. 3.3 - 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 1 Simplify polynomials in one variable by combining like terms.

3. 3.3 - 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Notice that the coefficient of the result, 5, is the sum of the coefficients of the like terms, 3 + 2 = 5. Because 5x has fewer symbols than 3x + 2x, we say we have simplified 3x + 2x, and 5x is in simplest form because it cannot be written with fewer symbols.

4. 3.3 - 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To combine like terms, add the coefficients and keep the variables and their exponents the same. Procedure

5. 3.3 - 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1 Combine like terms. a. 4x + 9x b. – 2y 3 – 5y 3 c. – 12n 2 + 7n 2 d. – 4m + 4m

6. 3.3 - 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Connection Adding measurements that have the same unit is like combining like terms. Suppose we have to calculate the perimeter of the rectangle shown. P = 4m + 10m + 4m + 10m P = 28m 4m4m 10m4m +10m + 4m + 10m = 28 Remember that we cannot add units that are not the same. We cannot combine cm (centimeters) and m (meters).

7. 3.3 - 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Why do we simplify expressions? It makes evaluating them easier…evaluate… – 12n 2 + 7n 2, when n = 2. Lets look at how we would do this if we didn’t combine like terms.

8. 3.3 - 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2 Combine like terms and write the resulting polynomial in descending order of degree.

9. 3.3 - 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 2 Add polynomials in one variable.

10. 3.3 - 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To add polynomials, combine like terms. Procedure Stack like terms to find the sum.

11. 3.3 - 11 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3 Add and write the polynomial in descending order of degree. a.

12. 3.3 - 12 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3 Add and write the polynomial in descending order of degree. b.

13. 3.3 - 13 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 3 Write an expression for the perimeter of a given shape.

14. 3.3 - 14 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 4 Write an expression in simplest form for the perimeter of the rectangle shown. 2x + 5 3x − 1

15. 3.3 - 15 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 4 Subtract polynomials in one variable.

16. 3.3 - 16 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley We can write polynomial subtraction as equivalent polynomial addition by changing the signs of each term in the subtrahend (second) polynomial.

17. 3.3 - 17 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To subtract polynomials: Procedure 1.Write the subtraction expression as an equivalent addition expression. a.Change the operation symbol from a – to a +. b.Change the subtrahend (second polynomial) to its additive inverse. To get the additive inverse, we change the sign of each term in the polynomial. 2.Combine like terms.

18. 3.3 - 18 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 5 Subtract and write the resulting polynomial in descending order of degree. a.