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Mathematics
OpenStudy (anonymous):

In the expansion of (x^3 - (2/x^2))^10, find the term in x^10, the coefficient of 1/x^5 and the constant term.

OpenStudy (anonymous):

\[(x^3 -\frac{2}{x^2})^{10}\]Right?

OpenStudy (anonymous):

yes :)

OpenStudy (anonymous):

okay Take \(\frac{1}{x^2}\) common and apply binomial expansion ah I don't remember the binomial expansion.

OpenStudy (anonymous):

i remember it. Tr+1 = (n,r) a^n-r * b^r. but i don't know which term will give me x^10. there could be terms added up and all, right?

OpenStudy (anonymous):

ah okay \[T_{r+1} = (n,r) a^{n-r}*b^r\]

OpenStudy (anonymous):

so we have \(\frac{1}{x^2}\) out that makes it \(\frac{1}{x^{20}}\)

OpenStudy (anonymous):

and the series expansion becomes \((x^5 + 2 )^{10}\) so we need x^15 here to make it \(\frac{1}{x^5}\)

OpenStudy (anonymous):

n-r = 3

OpenStudy (anonymous):

r = 7

OpenStudy (anonymous):

co-efficient is \((10,7)\frac{1}{x^5}*2^7\)

OpenStudy (anonymous):

exclude the x and you have the coefficient

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