How to find the coefficient of x^6y^8 in the Binomial Expansion of (2x^3-y^2)^6 ?

Q: How to find the coefficient of x^6y^8 in the Binomial Expansion of (2x^3-y^2)^6 ?Answer :Nth term in the Binomial Expansion of (2x^3-y^2)^6 will be given as $$=>\ \frac{n!}{k!\left(n-k\right)!}\left(2x^3\right)^{n-k}\left(-y^2\right)^k$$ $$=>\frac{n!}{\ k!\left(n-k\right)!}\left(-1\right)^k2^{n-k}x^{3n-3k}y^{2k}$$ We want the coefficient of x^6*y^8 that is $$=>3n-3k=6,\ 2k=8$$ $$=>k=4,\ n=6$$ Substituting n =6,…

This Question has been answered. 

Please Login or Register to See The Answer