Question

Complete the following statements in relation to the third term in the expansion of the binomial (2x+y^2)^5.

coefficient =
The power of x =
The power of y =

Answer 1

The binomial expansion of an expression is of the form


`(a+b)^n=\sum^n_(r=0){ ^nC_ra^rb^(n-r)`

Given the binomial expression


`(2x+y^2)^5`

The third term is when r = 2, thus the third term of the expanssion of the given expression is given by


`3rd\ term={ ^5C_2(2x)^2(y^2)^(5-2)} \\ \\ =10(4x^2)(y^2)^3=40x^2y^6`

Therefore, the coefficient = 40, the power of x = 2 and the power of y = 6.