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  4. The coefficient of x9 in the expansion of (1 + x + x2 + x3)3(1 - x)6 is

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Q. The coefficient of $x^9$ in the expansion of
$(1 + x + x^2 + x^3)^3(1 - x)^6$ is

Binomial Theorem

Solution:

Given expansion can be written as,
$(1 + x + x^2 + x^3)^3(1 - x)^3 (1 - x)^3$
$= (1 - x^4)^3(1 - x)^3$
$= (1 - 3x^4 + 3x^8 - x^{12}) (1 - 3x + 3x^2 - x^3)$
$\therefore $ The coefficient of $x^9$ is $3(-3) = - 9$.