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Find the coefficient of x3 in the binomial expansion ...

Find the coefficient of x3 in the binomial expansion of (x3x2)9.

A.

324

B.

252

C.

-252

D.

-324

Correct answer is A

x3x2=x3x2

Let the power on x be t, so that the power on x2 = 9 - t

(x)t(x2)9t=x3t18+2t=3

3t=3+18=21

To obtain the coefficient of x^{3}, we have

^{9}C_{7}(x)^{7}(3x^{-2))^{2} = \frac{9!}{(9 - 7)! 7!}(x)^{7}(9x^{-4})

= \frac{9 \times 8 \times 7!}{7! 2!} \times 9(x^{3}) = 324x^{3}