Copyright © 2008 Pearson Education, Inc Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

5.6 Special Products Square binomials. Find the product of the sum and difference of two terms. Find greater powers of binomials. 1 2 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Square binomials. Objective 1 Slide 5.6 - 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 3

Square binomials. The square of a binomial is a trinomial consisting of the square of the first term of the binomial, plus twice the product of the two terms, plus the square of the last term of the binomial. For x and y, Also, Notice that in the square of a sum, all of the terms are positive. In the square of a difference, the middle term is negative. A common error when squaring a binomial is to forget the middle term of the product. In general, Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 4

EXAMPLE 1 Find (x + 4)2. Solution: Squaring a Binomial Slide 5.6 - 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 5

EXAMPLE 2 Square each binomial and simplify. Solution: Squaring Binomials Square each binomial and simplify. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 6

Find the product of the sum and difference of two terms. Objective 2 Find the product of the sum and difference of two terms. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 7

Find the product of the sum and difference of two terms. In binomial products of the form (x + y)(x − y), one binomial is the sum of two terms and the other is the difference of the same two terms. Consider (x + 2)(x − 2). Thus, the product of x + y and x − y is the difference of two squares. The product rules of this section are essential as we continue to chapters 6 and 7. Remember and practice them. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 8

EXAMPLE 3 Find the product. Solution: Finding the Product of the Sum and Difference of Two Terms Find the product. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 9

EXAMPLE 4 Find each product. Solution: Finding the Product of the Sum and Difference of Two Terms Find each product. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 10

Find greater powers of binomials. Objective 3 Find greater powers of binomials. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 11

EXAMPLE 5 Find each product. Solution: Finding Greater Powers of Binomials Find each product. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.6 - 12