Question 369957
{{{f(x,y) = x^4 + 3x^2y^2 + y^4}}} Start with the given equation.



{{{f(ax,ay) = (ax)^4 + 3(ax)^2(ay)^2 + (ay)^4}}} Replace each 'x' with 'ax'. Replace each 'y' with 'ay'



{{{f(ax,ay) = a^4x^4 + 3a^2x^2a^2y^2 + a^4y^4}}} Use the property {{{(xy)^z=x^zy^z}}}



{{{f(ax,ay) = a^4x^4 + 3a^2*a^2x^2y^2 + a^4y^4}}} Rearrange the terms.



{{{f(ax,ay) = a^4x^4 + 3a^4x^2y^2 + a^4y^4}}} Multiply {{{a^2}}} and {{{a^2}}} to get {{{a^2*a^2=a^(2+2)=a^4}}}



{{{f(ax,ay) = a^4(x^4 + 3x^2y^2 + y^4)}}} Factor out the GCF {{{a^4}}}



{{{f(ax,ay) = a^4f(x,y)}}} Now replace the expression in the parenthesis with {{{f(x,y)}}} (this is possible since {{{f(x,y) = x^4 + 3x^2y^2 + y^4}}})