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  • 11. Find the coefficient of x^4 in the expansion of (1 + x + x^2 + x^3)^11.

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

Posted by

infoexpert22

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