Bionomials, Simplying. Radicals/ Add and subtract

On every problem, show all your computations, using the examples as guidelines. This is particularly important for the problems that have the answers given, as all the credit for these problems depends upon showing the correct computations.

CONJUGATES:

For each binomial, write its conjugate, and the product of the binomial and conjugate.

Examples:

Binomial

Conjugate

Product (Binomal Conjugate)

E1.

(a+b)

(a-b)

(a+b)(a-b)=a2-ab+ab-b2=a2-b2
ANS: a2-b2 (This is an important general result!)

E2.

; ANS: -1

Problems:

Binomial

Conjugate

Product (Binomal Conjugate)

1.

Ans: -1

2.

3.

4.

5.

RATIONALIZING DENOMINATORS. Remove the radical expression from the denominator of a fraction by multiplying both the numerator and the denominator by the conjugate of the denominator.

Examples:

E3. ANS:

E4. ANS:
Problems.

5.

6.

7.

8.

9.

10.

MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS: Perform the following operations.
Examples:

E5.

E6.

E7.
Problems:

11.

12.

13.

14.

15.
ADDING AND SUBTRACTING RADICAL EXPRESSIONS: Rationalize the expressions, as necessary, and then perform the indicated additions or subtractions.
Examples:

E8.

E9.
Problems:

16.

17.

18.

19.

20.
— end —

23
–
17
–
32
-+
52
-+
a3b2
+
11aa
a
aaa
æö
==
ç÷
ç÷
èø
a
a
(
)
(
)
213
22131
213
132
131313
–
æö
–
===–
ç÷
ç÷
–
++-
èø
(
)
1
213
2
—
42
Ans:6
3
6
2
3a
5
6
1
12
–
1
53
+
53
53
–
+
abab
c
c
=
(
)
3222323
-=-
22222
21
22
—
==-
35Ans:15
(
)
(
)
2637
12
+
182
(
)
2
25
(
)
(
)
1223
-+
11233223
236
23
+
+=+=
1113323
2236
3
–
-=-=
(
)
1131
Ans:321
22
2
–
-+-
112
2
2
–
+
112
1212
–
+
++
abb
2
aa
–
13
125
+
+
12
–
(
)
2
2
12121
-=-=-