Exponents, Polynomials, and Polynomial Functions Chapter 6 Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials 6.4 Multiplying Polynomials

6.4 Multiplying Polynomials Objectives Multiply terms. Multiply any two polynomials. Multiply binomials. Find the product of the sum and difference of two terms. Find the square of a binomial. Multiply polynomial functions. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying Monomials We multiply polynomials by using the distributive, commutative, and associative properties along with the rules of exponents. Multiply the numerical factors, then multiply the variable factors. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying a Polynomial by a Monomial To multiply a polynomial with more than one term by a monomial, use the distributive property to remove parentheses and simplify. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying a Binomial by a Binomial To multiply two binomials, multiply each term of one binomial by each term of the other binomial and combine like terms. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying the Product of Two Binomials by a Monomial Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying Polynomials Vertically Find the product. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Using the FOIL Method We can use a shortcut method, called the FOIL method, to multiply binomials. FOIL is an acronym for First terms, Outer terms, Inner terms, and Last terms. To use the FOIL method to multiply 2a – 4 by 3a + 5, we Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Using the FOIL Method First terms Last terms Inner terms Outer terms Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Product of the Sum and Difference of Two Terms Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Finding the Square of a Binomial Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Finding the Square of a Binomial Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Finding the Square of a Binomial Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying More Complicated Polynomials Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying Polynomial Functions In Section 6.3, we saw how functions could be added and subtracted. Functions can also be multiplied. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying Polynomial Functions Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.4 Multiplying Polynomials Multiplying Polynomial Functions Another way of arriving at the same answer is to find and then multiply the results to obtain –16. Copyright © 2010 Pearson Education, Inc. All rights reserved.