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