Question

Find each coefficent described.


Coeffecient of y^3 in expression of (2y+1)^6

Answer 1

The general expansion of (a+b)^n is given by
C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 +... C(n,n)b^n
where C(n,r) is the "n choose r" function,
C(n,r)=n!/(r!(n-r)!)

In the given case, to get the coefficient of y^3,
a=2y
b=1,
n=6,
r=3
C(6,3)(2y)^3(1)^(6-3)
=6!/(3!3!)2^3 y^3 1^3
=20*8y^3
=160y^3

Answer 2

Thanks though this is kinda confusing to me.