Question

How do you use the binomial theorem to expand and simplify the expression `(1/x+y)^5`?

Answer 1

`(1/x+y)^5=1/(x^5)+(5y)/x^4+(10y^2)/x^3+(10y^3)/x^2+(5y^4)/x+y^5`

Explanation:

`(1/x+y)^5`

=`(1/x)^5y^0*C(5,0)+(1/x)^4y^1*C(5,1)+(1/x)^3y^2*C(5,2)+(1/x)^2y^3*C(5,3)+(1/x)^1y^4*C(5,4)+(1/x)^0y^5*C(5,5)`

=`1/(x^5)+(5y)/x^4+(10y^2)/x^3+(10y^3)/x^2+(5y^4)/x+y^5`