Binomial TheoremHard

Question

The term independent of x in the binomial expansion of is :

Options

A.496
B.−496
C.400
D.−400

Solution

. 8Cr(2x2)8-r
= 8Cr(2x2)8-r 8Cr(2x2)8-r + 3x5 8Cr(2x2)8-r
= 8Cr 28-r(-1)r x16-3r - 8Cr 28-r(-1)r x15-3r + 3 8Cr 2(8 - r) (-1)r x21-3r
for independent term
16 - 3r = 0, 15 - 3r = 0, 21 - 3r = 0
r = 5,           r = 7 in III term
in II term
-8C5(23)(-1) - 3.8C7.2
= 448 - 6 × 8 = 448 - 48 = 400

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