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# Counting

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Find the positive integer n such that the expansion of (4x - 7y)^n contains a term of the form cx^2*y.

Mar 4, 2023

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Find the positive integer n such that the expansion of (4x - 7y)^n contains a term of the form cx^2*y.

General term is

$$\binom{n}{r}(4x)^r (-7y)^{n-r}\\ r=2,\\ n-2=1\qquad n=3\\~\\ \binom{3}{2}(4x)^2 (-7y)^{1}\\$$

Anyway,    n=3

Mar 4, 2023