Binomial TheoremHard
Question
If (1 + x + x2 + x3)5 = a0 + a1x + a2x2 +....................... + a15x15, then a10 equals to :If (1 + x + x2 + x3)5 = a0 + a1x + a2x2 +....................... + a15x15, then a10 equals to :
Options
A.99
B.101
C.100
D.110
Solution
(x4 - 1)5 (x - 1)-5
= 5C0 (x - 1)-5 - 5C1 x4 (x - 1)-5 + 5C2 x8 (x - 1)-5
= 5C0 × 14C4 - 5C1 × 10C6 + 5C2 × 6C2 = 101
= 5C0 (x - 1)-5 - 5C1 x4 (x - 1)-5 + 5C2 x8 (x - 1)-5
= 5C0 × 14C4 - 5C1 × 10C6 + 5C2 × 6C2 = 101
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