f(x+y) means to put x+y in for x in f(x)=x^2 - 3x
so f(x+y) = (x+y)^2 - 3(x+y) = (x+y)(x+y) - 3x - 3y
= x^2 + 2xy + y^2 - 3x - 3y then subtract f(x)
x^2 + 2xy + y^2 - 3x - 3y - (x^2 - 3x)
= x^2 + 2xy + y^2 - 3x - 3y - x^2 + 3x combine like terms and final answer is
=2xy + y^2 - 3y