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Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.
Answers (1)
Given: (1+x+x2+x3)11
That is equal to [(1+x) + x2(1 + x)]11
= [(1+x) (1+x2)]11
= (1+x)11.(1+x2)11
= (11C0 + 11C1x + 11C2x2 + 11C3x3 + 11C4x4 + ….) (11C0 + 11C1x2 + 11C2x4 + ….)
Thus, the coefficient of x4 =11C0 x 11C4 + 11C1 x 11C2+11C2x 11C0
= 330 + 605 + 55
= 990
View full answer
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