Math miscellaneousHard
Question
The coefficient of x7 in the expansion of (1 - x - x2 + x3)6 is
Options
A.- 132
B.- 144
C.132
D.144
Solution
[1 - x - x2 ( 1 - x)]6 = (1 - x)6 (1 - x2)6
= [6C0 - 6C1x + 6C2x2 - 6C3x3 + 6C4x4 - 6C5x5 + 6C6x6] × [6C0 - 6C1x + 6C2x2 - 6C3x3 + .....]
Coefficient of x7 = 6C1 6C3 6C3 6C2 + 6C5 6C1 = 120 ″300 + 36 = 144
= [6C0 - 6C1x + 6C2x2 - 6C3x3 + 6C4x4 - 6C5x5 + 6C6x6] × [6C0 - 6C1x + 6C2x2 - 6C3x3 + .....]
Coefficient of x7 = 6C1 6C3 6C3 6C2 + 6C5 6C1 = 120 ″300 + 36 = 144
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