Beginning Algebra, 11th Edition

OBJECTIVE 1 Simplify products of radical expressions.

Multiplying Radical Expressions

Find each product and simplify.

(a)

Subtract like radicals.

Product rule

=- 2210 Multiply.

=- 225 # 2

= (^25) A- (^222) B

= 25 A 222 - 422 B 28 = 222 ; 232 = 422

(^25) A 28 - (^232) B
EXAMPLE 1
524 CHAPTER 8 Roots and Radicals
Simplify inside
the parentheses.
(b)
First Outer Inner Last
Product rule
Add like radicals. Multiply.
=- 37 - 2215 Combine like terms.

= 3 - 2215 - 40

= 3 - 4215 + 2215 - 8 # 5

= (^23) A (^23) B + (^23) A- (^425) B+ (^225) A (^23) B + (^225) A- (^425) B

A 23 + 225 BA 23 - 425 B

(c)

FOIL

Product rule

= 3 - 221 + 327 - 723 29 =3; 249 = 7

= 3 - 221 + 29 # 27 - 249 # 23

= 3 - 221 + 263 - 2147

= 23 A 23 B + 23 A- 27 B + 221 A 23 B+ 221 A- 27 B

A^23 +^221 BA^23 -^27 B

⎧⎪⎨⎪⎩ ⎧ ⎪ ⎨ ⎪ ⎩ ⎧⎪⎨⎪⎩ ⎧ ⎪ ⎨ ⎪ ⎩

Use the FOIL

method to multiply.

This does not

equal - 39215.

Factor; 9 and 49 are

perfect squares.

Since there are no like radicals, no terms can be combined. NOW TRY

Example 2uses the rules for the square of a binomial from Section 5.6.

and

Using Special Products with Radicals

Find each product. Assume that

(a)

= 59 - 14210 Combine like terms.

= 10 - 14210 + 49 A 210 B^2 =10; 7^2 = 49

= A (^210) B^2 - (^2) A (^210) B 172 + 72

A 210 - 7 B

2

xÚ0.

EXAMPLE 2

1 xy 22 x^2  2 xyy^21 xy 22 x^2  2 xyy^2

NOW TRY
EXERCISE 1
Find each product and simplify.

(a)

(b)

(c) A 210 - 8 BA 2210 + 322 B

A 223 + 27 BA 23 + 327 B

23 A 245 - 220 B

Do nottry

to combine

further here.

NOW TRY ANSWERS

1. (a)
   (b)
   (c) 20 + 625 - 16210 - 2422

27 + 7221

215

Let and x= 210 y=7.

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

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