CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 8 – Binomial Theorem Maths
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Exercise 8.1
Book Name: NCERT Solutions
Question 1:
Expand the expression 5
1
2x
Solution 1:
By using Binomial Theorem, the expression 5
can be expanded as 5
1
2x
1
2x
5 5 5 4 5 3 2 5 2 3 5 1 4 5
5
C0 1 C1 1 2x C2 1 2x C3 1 2x C4 1 2x C5
2x
x x 2 x 3 x 4 x
5
1 5 2 10 4 10 8 5 16 32
110x 40x 80x 80x 32x
2 3 4 5
Question 2:
Expand the expression
Solution 2:
2
x
x 2
By using Binomial Theorem, the expression
5
2
x
x 2
5
can be expanded as
5 5 4 3 2 2 3 4 5
5 5 5 5 5 5
C0 C1 C2 C3 C4 C5
2 x 2 2 x 2 x 2 x 2 x x
x 2 x x 2 x 2 x 2 x 2 2
2 3 4 5
32 16 x 8 x 4 x 2 x x
5 10 10 5
3 4 3 2
x x 2 x 4 x 8 x 16 32
32 40 20 5 5
x
x x x 8 32
3
5x x
5 3
Question 3:
Expand the expression 2x 3 6
Solution 3:
By using Binomial Theorem, the expression 2x 3 6
can be expanded as
6 6 6 6 5 6 4 2 6 3 3 6 2 4 6 5 6 6
0 1 2 3 4 5 6
2x 3 C 2x C 2x 3 C 2x 3 C 2x 3 C 2x 3 C 2x 3 C 3
6 5 4 3 2
64x 6 32x 3 15 16x 9 20 8x 27 15 4x 81 6 2x
243 729
6 5 4 3 2
64x 576x 2160x 4320x 4860x 2916x
729
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