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Answer :
512 is the coefficient of the x9y-term
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Answer:- 512
Explanation:-
We know that [tex](m+1)^{th},\ (T_{m+1})[/tex] in the binomial expansion [tex](p+q)^n[/tex] is given by
[tex]T_{m+1}=^nC_m\ p^{n-m}q^m[/tex]
Assume that [tex]x^9y[/tex] occurs in the [tex](m+1)^{th}[/tex] term of the expansion of [tex](2y+4x^3)^4=(4x^3+2y)^4[/tex]
[tex]T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m[/tex]
Comparing power of x and y in [tex]x^9y[/tex] we get m=1
Thus term for m=1 [tex]=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y[/tex]
Thus the coefficient of [tex]x^9y[/tex] is 512.
