Find the Constant Term In (x^2 - 2/x)^9 | Olympiad Math

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We use the binomial formula to obtain the general term in the expansion of (x^2-2/x)^9. Then we find the correct k such that in the kth term, the power of the x term is zero.

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Without looking at the video, I reasoned the following:
x^2 adds 2 to the power of x, 2/x subtracts 1 from the power of x, so
Using 9 terms of either +2 or -1, the only way to get 0 is +2 +2 +2, -1 -1 -1 -1 -1 -1. Multiplied together, this term is 2^6.x^0 = 64.
In the expanded product, there are 9 choose 3 terms with these products, that is 9!/6!/3! = 84 terms.
The sum of these terms is 84 * 64 = 5376.

morganga
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Not clear, what is mean by constant term in this case?

bikramjitsanyal