Beginning Algebra, 11th Edition

(e)

Square the binomial.

Distributive property NOW TRY

In the square of a sum, all of the terms are positive,as in Examples 2(b) and

(d).In the square of a difference, the middle term is negative,as in Examples 2(a),

(c), and (e).

= 16 x^3 - 24 x^2 + 9 x

= x 116 x^2 - 24 x+ 92

x 14 x- 322

OBJECTIVE 2 Find the product of the sum and difference of two terms.

In binomial products of the form , one binomial is the sum of two

terms and the other is the difference of the sametwo terms. Consider

FOIL

Combine like terms.

Thus, the product of x+yand x- yis the difference of two squares.

= x^2 - 4

= x^2 - 2 x+ 2 x- 4

1 x+ 221 x- 22

1 x+ 221 x- 22.

1 x+y 21 x-y 2

CAUTION A common error when squaring a binomial is to forget the middle

term of the product. In general,

and 1 x-y 22 =x^2 - 2 xy+y^2 , not x^2 - y^2.

1 x+y 22 =x^2 + 2 xy+y^2 , not x^2 + y^2 ,

Product of the Sum and Difference of Two Terms

1 xy 21 xy 2 x^2 y^2

Finding the Product of the Sum and Difference of Two Terms

Find each product.

(a)

Use the rule for the product of the sum and difference of two terms.

(b)

Commutative property

= Square.^23 NOW TRY

4

9

- w^2

= a 1 x+y 21 x-y 2 =x^2 - y^2

2

3

b

2

- w^2

= a

2

3

+wba

2

3

- wb

a

2

3

- wba

2

3

+wb

= x^2 - 16

= x^2 - 42

1 x+ 421 x- 42

1 x+ 421 x- 42

NOW TRY EXAMPLE 3

EXERCISE 3
Find the product.

1 t+ 1021 t- 102

3.t^2 - 100

336 CHAPTER 5 Exponents and Polynomials

NOW TRY
EXERCISE 2
Find each binomial square
and simplify.

(a)

(b)

(c)

(d)m 12 m+ 322

A 6 t-^13 B

2

14 p- 5 q 22

13 x- 122

NOW TRY ANSWERS

2. (a)
   (b)
   (c)
   (d) 4 m^3 + 12 m^2 + 9 m

36 t^2 - 4 t+^19

16 p^2 - 40 pq+ 25 q^2

9 x^2 - 6 x+ 1

Remember the middle term.

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