Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 5.4 Multiplying Polynomials.

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Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 5.4 Multiplying Polynomials

2 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplying a Monomial by a Polynomial We use the distributive property to multiply a monomial by a polynomial. Remember the distributive property states that for a real numbers a, b, and c, a(a + c) = ab + ac.

3 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Use the distributive property to multiply a monomial by a polynomial. a. Multiply. 3(c – 4) 3(c – 4) = 3(c) + 3(– 4) = 3c – 12 b. Multiply. 2x 3 (x 2 – x + 2) 2x 3 (x 2 – x + 2) = 2x 3 (x 2 ) + 2x 3 (– x) + 2x 3 (2) = 2x 5 – 2x 4 + 4x 3 Example

4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplying Two Binomials To multiply two binomials, the distributive property is used so that every term in one polynomial is multiplied by every term in the other polynomial.

5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiply. (7x + 3)(2x + 4) This method used to multiply two binomials is referred to as the FOIL method. = 14x 2 + 6x + 28x + 12 = 14x x + 12 (7x + 3)(2x + 4) = (7x + 3)(2x) + (7x + 3)(4) Example

6 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Consider (a + b)(c + d): FOILFOIL FOILFOIL “First” (a + b) (c + d) F “Outer” (a + b) (c + d) O “Inner” (a + b) (c + d) I “Last” L (a + b) (c + d) The product of the two binomials is the sum of these four products: (a + b)(c + d) = ac + ad + bc + bd The FOIL Method Multiply the first terms together. Multiply the outer terms together. Multiply the inner terms together. Multiply the last terms together. product ac product ad product bc product bd

7 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiply using the FOIL method. (7x + 3)(2x + 4) = (7x)(2x) (7x + 3)(2x + 4) F F O O + (7x)(4) + (3)(2x) I I + (3)(4) L L = 14x x + 6x + 12 = 14x x + 12 Example

8 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiply. (3x + 4)(5x  y) = (3x)(5x) + (3x)(  y) + (4)(5x) + (4)(  y) F O I L (3x + 4)(5x  y) = 15x 2 + (  3xy) + 20x + (  4y) = 15x 2  3xy + 20x  4y Example

9 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiply. Example

10 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. The width of a living room is (x + 4) feet. The length of the room is (3x + 5) feet. What is the area of the room in square feet? Example There are (3x x + 20) square feet in the room.