12Brady 12Brady

13-07-2017
Mathematics

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binomial theorem help me solve x^5 Y^8 (x+y)^13

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LammettHash LammettHash

13-07-2017

I assume you're asking to find the coefficient of the [tex]x^5y^8[/tex] term in the expansion of [tex](x+y)^{13}[/tex].

The binomial theorem says that the expansion itself is

[tex]\displaystyle(x+y)^{13}=\sum_{k=0}^{k=13}\binom{13}kx^{13-k}y^k[/tex]

and we obtain the [tex]x^5y^8[/tex] term when [tex]k=8[/tex]. So the coefficient of this term would be

[tex]\dbinom{13}8=\dfrac{13!}{8!(13-8)!}=1287[/tex]

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