Exercise 8.2
Find the coefficient of
Q1. x5 in (x + 3)8
Solution:
(x + 3)8
General term nCr an-r br
n = 8, then
8Cr x8-r 3r ⇒ x5 = x8-r
5 = 8-r
∴ r = 8-5 = 3
8C3 x8-3 33 = 8C3 x5 33
Coefficient in x5 = 8C3 33
= 1512
Q2. a5b7 in (a-2b)12
Solution:
(a-2b)12
General Term Tr+1 = nCr an-r br
12Cr a12-r br
∴12 – r = 5 ⇒ r = 12 – 5 = 7
a5b7 is 8 term
T8 = 12C7 a5 b7
= 12C7 a5 (-2b)7
= - 72 × 11 × 27
= - 72 × 11 × 128 = - 101376
Write the general term in the expansion of
Q3. (x2 - y)6
Solution:
General term of (x2 - y)6
n = 6, a = x2, b = (-y)
General Term Tr +1 = nCr an-r br
= 6Cr (x2)6-r (-y)r
=
