Question

If f(x,y) = x^3 + 4xy^2 + y^3, show that f(ax, ay)= a^3 f(x,y).

Answer 1

$f(ax, ay) = (ax)^3 + 4 ax(ay )^2+(ay)^3 = a^3x^3+4a^3xy^2 + a^3y^3 = a^3(x^3+4xy^2+y^3) = a^3f(x,y)$