Beginning Algebra, 11th Edition

SECTION 5.6 Special Products^335

OBJECTIVES OBJECTIVE 1 Square binomials.The square of a binomial can be found

quickly by using the method suggested by Example 1.

Squaring a Binomial

Find

FOIL

= m^2 + 6 m+ 9

= m^2 + 3 m+ 3 m+ 9

1 m+ 321 m+ 32

1 m+ 322.

EXAMPLE 1

Special Products

5.6

1 Square binomials.

2 Find the product

of the sum and

difference of two

terms.

3 Find greater powers

of binomials.

NOW TRY
EXERCISE 1
Find. 1 x+ 522

NOW TRY ANSWER

1. x^2 + 10 x+ 25

Square of a Binomial

The square of a binomial is a trinomial consisting of

Squaring Binomials

Find each binomial square and simplify.

(a)

(b)

= 9 b^2 + 30 br+ 25 r^2

= 13 b 22 + 213 b 215 r 2 + 15 r 22

13 b+ 5 r 22

= 25 z^2 - 10 z+ 1 15 z 22 = 52 z^2 = 25 z^2

15 z - 122 = 15 z 22 - 215 z 2112 + 1122

1 x- y 22 = x^2 - 2 #x#y + y^2

EXAMPLE 2

Combine like terms.

This is the answer.

means

1 m+ 321 m+ 32.

1 m+ 322

This result has the squares of the first and the last terms of the binomial.

and

The middle term, 6m, is twice the product of the two terms of the binomial,since the

outer and inner products are and Then we find their sum.

m 132 + 31 m 2 = 21 m 2132 = 6 m NOW TRY

m 132 31 m 2.

m^2 = m^232 = 9

(c)

= 4 a^2 - 36 ax+ 81 x^2

= 12 a 22 - 212 a 219 x 2 + 19 x 22

12 a- 9 x 22

(d)

= 16 m^2 + 4 m+

1

4

= 14 m 22 + 214 m2a

1

2

b + a

1

2

b

2

a 4 m+

1

2

b

2

For xand y, the following are true.

1 xy 22 x^2  2 xyy^2

1 xy 22 x^2  2 xyy^2

the square of

the first term +

twice the product

of the two terms +

the square of

the last term.