Bionomials, Simplying. Radicals/ Add and subtract
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119980mat101_slp2_spr13.docx
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:
Problems.
MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS: Perform the following operations.
Examples:
Problems:
ADDING AND SUBTRACTING RADICAL EXPRESSIONS: Rationalize the expressions, as necessary, and then perform the indicated additions or subtractions.
Examples:
Problems:
--- 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
-=-=-
