Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Simplifying, Adding, and Subtracting Polynomials 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.

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

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, = 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.

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

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

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).

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.

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.

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

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

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

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

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

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

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

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.

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.

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