The binomial expansion of an expression is of the form
[tex](a+b)^n=\sum^n_{r=0}{ ^nC_ra^rb^{n-r}[/tex]
Given the binomial expression
[tex](2x+y^2)^5[/tex]
The third term is when r = 2, thus the third term of the expanssion of the given expression is given by
[tex]3rd\ term={ ^5C_2(2x)^2(y^2)^{5-2}} \\ \\ =10(4x^2)(y^2)^3=40x^2y^6[/tex]
Therefore, the coefficient = 40, the power of x = 2 and the power of y = 6.
