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Multiplying Polynomials; Special Products 5.5 1.Multiply a polynomial by a monomial. 2.Multiply binomials. 3. Multiply polynomials. 4.Determine the product when given special polynomial factors.

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Objective 1 Multiply a polynomial by a monomial.

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Multiply. 2p 6p 2 2p 2p –1 2p ∙ 6p 2 + 2p ∙ 2p+ 2p ∙ – 1

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Multiplying a Polynomial by a Monomial Use the distributive property to multiply each term in the polynomial by the monomial.

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When an equation in one variable is solved the answer is a point on a line. Multiply:

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Objective 2 Multiply binomials.

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Multiply. 7 x 7 3 x 3 x

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Multiplying Polynomials 1. Multiply every term in the second polynomial by every term in the first polynomial. 2. Combine like terms.

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Multiply. FOIL: First Outside Inside Last FirstOutsideInside Last 1 x Inside 1 (–5) Last 2x (–5) Outside 2x x First

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When an equation in one variable is solved the answer is a point on a line. Multiply:

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The product of two binomials can be shown in terms of geometry. 35 5x5x 7x7xx2x2 Length width = Sum of the areas of the four internal rectangles Combine like terms. 5 x x 7

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Objective 3 Multiply polynomials.

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Multiply. (–3) 2x 2 (–3) 3x (–3) 3 x 2x 2 x 3xx 3 Horizontal Multiplication

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Multiply. Vertical Multiplication

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When an equation in one variable is solved the answer is a point on a line. Multiply:

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Objective 4 Determine the product when given special polynomial factors.

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When an equation in one variable is solved the answer is a point on a line. Multiply:

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Multiplying Conjugates If a and b are real numbers, variables, or expressions, then (a + b)(a – b) = a 2 – b 2. Conjugates: Binomials that differ only in the sign separating the terms. x + 9 and x – 9 2x + 3 and 2x – 3 –6x + 5 and –6x – 5

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When an equation in one variable is solved the answer is a point on a line. Multiply: 2 ∙ 4a 2 ∙ – 5 n

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Squaring a Binomial If a and b are real numbers, variables, or expressions, then (a + b) 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 – 2ab + b 2 or rewrite and foil !! Remember the shortcut

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When an equation in one variable is solved the answer is a point on a line. Multiply:

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Slide 5- 22 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

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Slide 5- 23 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

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Slide 5- 24 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

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Slide 5- 25 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

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