chapter 5 section 6 copyright © 2008 pearson education, inc. publishing as pearson addison-wesley
TRANSCRIPT
Chapter Chapter 55Section Section 66
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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5.65.65.65.6Square binomials.Find the product of the sum and difference of two terms.Find greater powers of binomials.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 11
Square binomials.
Slide 5.6 - 3
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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,
Slide 5.6 - 4
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.
2 2 2.2x y x xy y
2 2 2.2x y x xy y
A common error when squaring a binomial is to forget the middle term of the product. In general,
2 2 2 2 2, not2 x y x xy y x y
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 1
Solution:
Squaring a Binomial
Find (x + 4)2.
4 4x x
Slide 5.6 - 5
2 4 4 16x x x 2 8 16x x
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EXAMPLE 2
Solution:
Squaring Binomials
Square each binomial and simplify.
22 1x
Slide 5.6 - 6
25 6r s
21
32
k
22 7x x
24 2 2 1x x x 2 1 2 1x x 24 4 1x x
5 6 5 6r s r s 2 225 30 30 36r rs rs s 2 225 60 36r rs s
2 7 2 7x x x 24 14 14 49x x x x
24 28 49x x x 3 24 28 49x x x
1 13 3
2 2k k
2 3 3 1
92 2 4
k k k
2 19 3
4k k 2 6 1
92 4
k k
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 22
Find the product of the sum and difference of two terms.
Slide 5.6 - 7
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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).
Slide 5.6 - 8
22 2 2 2 4x x x x x
Thus, the product of x + y and x − y is the difference of two squares.
2 2– –x + y x y x y
2 4x
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
EXAMPLE 3Finding the Product of the Sum and Difference of Two Terms
Find the product.
Slide 5.6 - 9
Solution:
3 3y y
2 23 y
29 y
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 4
Find each product.
Finding the Product of the Sum and Difference of Two Terms
Slide 5.6 - 10
10 7 10 7m m
1 13 3
2 2r r
6 5 6 5x x x
2100 49m 2 210 7m
2
2 13
2r
2 1
94
r
2 26 5x x 236 25x x
336 25x x
Solution:
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 33
Find greater powers of binomials.
Slide 5.6 - 11
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 5
Solution:
Finding Greater Powers of Binomials
Find each product.
34 1x 2
4 1 4 1x x
2 23 2 3 2k k
Slide 5.6 - 12
43 2k
216 8 1 4 1x x x 3 2 264 32 4 16 8 1x x x x x 3 264 48 12 1x x x
2 29 12 4 9 12 4k k k k
4 3 2 3 2 281 108 36 108 144 48 36 48 16k k k k k k k k 4 3 281 216 216 96 16k k k k