CHAPTER 12 Polynomials: Operations Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 12.1Integers as Exponents 12.2Exponents and Scientific Notation 12.3Introduction to Polynomials 12.4Addition and Subtraction of Polynomials 12.5Multiplication of Polynomials 12.6Special Products 12.7Operations with Polynomials in Several Variables 12.8Division of Polynomials

OBJECTIVES 12.5 Multiplication of Polynomials Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aMultiply monomials. bMultiply a monomial and any polynomial. cMultiply two binomials. dMultiply any two polynomials.

12.5 Multiplication of Polynomials Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To find an equivalent expression for the product of two monomials, multiply the coefficients and then multiply the variables using the product rule for exponents.

EXAMPLE 12.5 Multiplication of Polynomials a Multiply monomials. 3 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

12.5 Multiplication of Polynomials Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply a monomial and a polynomial, multiply each term of the polynomial by the monomial.

EXAMPLE 12.5 Multiplication of Polynomials b Multiply a monomial and any polynomial. 6 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 12.5 Multiplication of Polynomials c Multiply two binomials. 8 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 12.5 Multiplication of Polynomials d Multiply any two polynomials. 9 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

12.5 Multiplication of Polynomials Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply two polynomials P and Q, select one of the polynomials—say, P. Then multiply each term of P by every term of Q and collect like terms.

EXAMPLE 12.5 Multiplication of Polynomials d Multiply any two polynomials. 10 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 12.5 Multiplication of Polynomials d Multiply any two polynomials. 12 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When missing terms occur, it helps to leave spaces for them and align like terms as we multiply.