Intermediate Algebra (11th edition)

Squaring Binomials

Find each product.

(a)

(b)

= p^2 - 8 p+ 16

= p^2 - 2 #p# 4 + 42 1 x-y 22 =x^2 - 2 xy+y^2

1 p- 422

= m^2 + 14 m+ 49

= m^2 + 2 #m# 7 + 72 1 x+y 22 =x^2 + 2 xy+y^2

1 m+ 722

EXAMPLE 6

SECTION 5.4 Multiplying Polynomials 297

Square of a Binomial

The square of a binomialis the sum of the square of the first term, twice the

product of the two terms, and the square of the last term.

1 xy 22 x^2  2 xyy^2

1 xy 22 x^2  2 xyy^2

(c) (d)

= 9 r^2 - 30 rs+ 25 s^2

= 13 r 22 - 213 r 215 s 2 + 15 s 22

13 r - 5 s 22

= 4 p^2 + 12 pv+ 9 v^2

= 12 p 22 + 212 p 213 v 2 + 13 v 22

12 p+ 3 v 22

CAUTION As the products in the formula for the square of a binomial show,

More generally,

Multiplying More Complicated Binomials

Find each product.

(a)

Product of sum and difference of terms

Square both quantities.

(b)

Square of a binomial

(c)

Square

Distributive property

= x^3 + 3 x^2 y+ 3 xy^2 + y^3 Combine like terms.

= x^3 + 2 x^2 y+ xy^2 +x^2 y+ 2 xy^2 +y^3

= 1 x^2 + 2 xy+y^221 x+ y 2 x+y.

= 1 x+ y 221 x+y 2 a^3 =a^2 #a

1 x+y 23

= 4 z^2 + 4 zr+r^2 + 4 z+ 2 r + 1

= 12 z+r 22 + 212 z+r 2112 + 12

312 z+r 2 + 142

= 9 p^2 - 12 p+ 4 - 25 q^2

= 13 p- 222 - 15 q 22

313 p- 22 + 5 q 4313 p- 22 - 5 q 4

EXAMPLE 7

1 x+y 2 nZxn+ yn 1 nZ 12.

1 x+ y 22 Zx^2 +y^2.

NOW TRY

NOW TRY
EXERCISE 6
Find each product.

(a) 1 y- 1022 (b) 14 x+ 5 y 22

NOW TRY ANSWERS

6. (a)
   (b) 16 x^2 + 40 xy+ 25 y^2

y^2 - 20 y+ 100

This does

not equal

x 3 +y 3.

Square again. Use the

distributive property.