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# What is the coefficient of a^4b^2 in the expansion of (2a-b/3)^6? Express your answer as a common fraction.

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What is the coefficient of  a^4b^2 in the expansion of (2a-b/3)^6? Express your answer as a common fraction.

Aug 6, 2017

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What is the coefficient of  a^4b^2 in the expansion of (2a-b/3)^6? Express your answer as a common fraction.

$$(2a-\frac{b}{3})^6=\displaystyle\sum_{n=0}^6\binom{6}{n}\left(\frac{-b}{3}\right)^n*(2a)^{6-n}\\~\\ so\;\;the\;\; a^4b^2\;\; term\;\; is\\~\\ \binom{6}{2}\left(\frac{-b}{3}\right)^2*(2a)^{6-2}\\ =15*\frac{b^2}{3^2}*2^4a^{4}\\ =5*\frac{b^2}{3}*16a^{4}\\ =\frac{80}{3}a^{4}b^2\\~\\ \text{The coefficient is 80/3}$$

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Aug 6, 2017