Chapter 5 Section 5
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Multiply a monomial and a polynomial. Multiply two polynomials. Multiply binomials by the FOIL method Copyright © 2012 Pearson Education, Inc. Multiplying Polynomials
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Multiply a monomial and a polynomial. Slide 5.5-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc. To find the product of a monomial and a polynomial with more than one term we use the distributive property and multiplication of monomials. Multiply a monomial and a polynomial. As shown in Section 5.1, we find the product of two monomials by using the rules for exponents and the commutative and associative properties. For example Do not confuse addition of terms with multiplication of terms. For instance, but Slide 5.5-4
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Find the product. Slide EXAMPLE 1 Multiplying Monomials and Polynomials
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Multiply two polynomials. Slide 5.5-6
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply two polynomials. We can use the distributive property repeatedly to find the product of any two polynomials. For example, to find the product of the polynomials x 2 + 3x +5 and x − 4, think of x − 4 as a single quantity and use the distributive property as follows. Now use the distributive property three more times to find x 2 (x − 4), 3x(x − 4), and 5(x − 4). Multiplying Polynomials To multiply two polynomials, multiply each term of the second polynomial by each term of the first polynomial and add the products. Slide 5.5-7
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply (m 3 − 2m + 1)·(2m 2 + 4m + 3). Solution: Slide EXAMPLE 2 Multiplying Two Polynomials
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply. Solution: Slide EXAMPLE 3 Multiplying Polynomials Vertically
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply. Solution: Slide EXAMPLE 4 Multiplying Polynomials with Fractional Coefficients Vertically
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Multiply binomials by the FOIL method. Slide
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply binomials by the FOIL method. In algebra, many times the polynomials to be multiplied are binomials. For these products, the FOIL method reduces the rectangle method to a systematic approach without the rectangle. Multiplying Binomials by the FOIL Method Step 1: Multiply the two First terms of the binomials to get the first term of the answer. Step 2: Find the Outer product and Inner product and add them (when possible) to get the middle term of the answer. Step 3: Multiply the two Last terms of the binomials to get the last term of the answer. Slide
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the FOIL to find the product. Solution: Slide EXAMPLE 5 Using the FOIL Method
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiply Solution: Slide EXAMPLE 6 Using the FOIL Method
Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find each product. Solution: Slide EXAMPLE 7 Using the FOIL Method