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Find the coefficient of x^(13) in the ex...

Find the coefficient of `x^(13)` in the expansion of `(1-x)^5xx(1+x+x^2+x^3)^4dot`

Text Solution

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`E = (1-x)^(5)(1-+x)^(4) (1+x^(2))^(4)`
`= (1-x)(1-x^(2))^(4)(1+x^(2))^(4)`
` = (1-x)(1-x^(4))^(4)`
` = (1-x)[1-4(x^(4))+6(x^(4))^(2) - 4(x^(4))^(3)+(x^(4))^(4)]`
Coefficient of `x^(13)` is `(-1)(-4) = 4`
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