ILLUSTRATION 8.1 Simplify the expression x+10x'a + 40x'a+ 80xa -+80xa +32a.
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Answer:
Binomial Expansion for positive Integral
Index -
Simplify: x
5
+10x
4
a+40x
3
a
2
+80x
2
a
3
+80xa
4
+32a
5
binomial expansion of (x+a)
n
=
n
C
0
x
n
+
n
C
1
x
n−1
a+...
....+
n
C
r
x
n−r
a
r
+...
+
n
C
n
x
.
a
n
Now,
(x+2a)
5
=
5
C
0
x
5
+
5
C
1
x
4
(2a)+
5
C
2
x
3
(2a)
2
+
5
C
3
x
2
(2a)
3
+
5
C
4
(2a)
4
x+
5
C
5
(2a)
5
(x+2a)
5
=x
5
+10ax
4
+10×4a
2
x
3
+10×8a
3
x
2
+5×16a
4
x+32a
5
(x+2a)
5
=x
5
+10x
4
a+40x
3
a
2
+80x
2
a
3
+80xa
4
+32a
5
Step-by-step explanation:
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