expand the binomial (1-3x)^ 5 upto the term having x^3
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Answer:
Let y=x+x
2
Then, (1+x+x
2
)
3
=(1+y)
3
=
3
C
0
+
3
C
1
+
3
C
1
+
3
C
2
y
2
+
3
C
3
y
3
=1+3y+3y
2
+y
3
=1+3(x+x
2
)+3(x+x
2
)
2
+(x+x
2
)
3
=1+3(x+x
2
)+3(x
2
+2x
3
+x
4
)+{
3
C
0
x
3
x
2
)
0
+
3
C
1
(x
2
)x
2
)
1
+
3
C
2
x
1
(x
2
)
2
+
3
C
3
(x
2
)
3
}
=1+3(x+x
2
)+3(x
2
+2x
3
+x
4
)+(x
3
+3x
4
+3x
5
+x
6
)
=x
6
+3x
5
+6x
4
+7x
3
+6x
2
+3x+1.
Explanation:
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