Intermediate Algebra (11th edition)

Multiplying Binomials Involving Radical Expressions

Multiply, using the FOIL method.

(a)

First Outer Inner Last

= 230 + 25 + 326 + 3

= 25 # 26 + 25 # 1 + 3 # 26 + 3 # 1

A 25 + 3 BA 26 + 1 B

EXAMPLE 1

458 CHAPTER 8 Roots, Radicals, and Root Functions

OBJECTIVES OBJECTIVE 1 Multiply radical expressions. We multiply binomial expres-

sions involving radicals by using the FOIL method from Section 5.4.Recall that the

acronym FOILrefers to multiplying the First terms, Outer terms, Inner terms, and

Last terms of the binomials.

Multiplying and Dividing Radical Expressions

8.5

1 Multiply radical

expressions.

2 Rationalize

denominators with

one radical term.

3 Rationalize

denominators with

binomials involving

radicals.

4 Write radical

quotients in lowest

terms.

⎩⎪⎨⎪⎧ ⎩⎪⎨⎪⎧ ⎩⎪⎨⎪⎧ ⎩⎨⎧

This result cannot be

simplified further.

(e)

= 25 - 239

= 25 - 2332

= 5 # 5 + 5233 - 5233 - 233 # 233

A^5 -^233 BA^5 +^233 B

Be careful. These

terms cannot be

combined.

Remember to

write the index 3

in each radical.

(b)

FO I L

(c)

FOIL

The product is the difference

of squares.

Here, and

(d)

= 16 - 627

= 7 - 627 + 9

= 27 # 27 - 327 - 327 + 3 # 3

= A 27 - (^3) BA 27 - (^3) B

A^27 -^3 B

2

1 xy 21 xy 2 x^2 y^2 x= 210 y= 23.

A^210 +^23 BA^210 -^23 B = A^210 B

2

• A (^23) B
  2

= 7

= 10 - 3

= 210 # 210 - 210 # 23 + 210 # 23 - 23 # 23

A^210 +^23 BA^210 -^23 B

= 725 + 722 - 215 - 26

= 725 + 722 - 23 # 25 - 23 # 22

A^7 -^23 BA^25 +^22 B