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

Objective 1 Multiply a polynomial by a monomial.

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

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

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

Objective 2 Multiply binomials.

Multiply. 7 x 7 3 x 3 x

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

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

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

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

Objective 3 Multiply polynomials.

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

Multiply. Vertical Multiplication

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

Objective 4 Determine the product when given special polynomial factors.

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

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

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

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

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

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

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

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

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