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  4. The coefficient of x8 in the expression (2+x)2(3+x)3(4+x)4 must be

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Q. The coefficient of $x^8$ in the expression $(2+x)^2(3+x)^3(4+x)^4$ must be

Binomial Theorem

Solution:

The expression $(2+x)^2(3+x)^3(4+x)^4$
$=(x+2)(x+2)(x+3)(x+3)(x+3)(x+4)(x+4)(x+4)(x+4)$
$= x ^9+(2+2+3+3+3+4+4+4+4) x^8+\ldots \ldots \ldots \ldots$.
Co-efficient of $x^8=29$