Math is our friend! Treat it PROPERLY!

The most important person in my life was deceived by a lying website. It said "(X^2 + Y^2 -1)^3 = X^2Y^3 When plotted, the equation makes a curve in the shape of a heart."

Well, that is a lie. I had to give the correct answer to (X^2 + Y^2 -1)^3. It most definitely does NOT equal X^2Y^3! So here is the correct answer with the steps provided to help anyone who cares to read this to follow along.

(X^2 + Y^2 -1)^3 =

(X^2 + Y^2 - 1) * (X^4 + X^2Y^2 - X^2 + X^2Y^2 + Y^4 - Y^2 - X^2 - Y^2 + 1) =

(X^2 + Y^2 - 1) * (X^4 +2X^2Y^2 + Y^4 - 2X^2 - 2Y^2 + 1) =

X^6 + 2X^4Y^2 + X^2Y^4 - 2X^4 - 2X^2Y^2 + X^2 + X^4Y^2 + 2X^2Y^4 + Y^6 - 2X^2Y^2 - 2Y^4 + Y^2 - X^4 - 2X^2Y^2 - Y^4 + 2X^2 + 2Y^2 - 1 =

X^6 + 3X^4Y^2 + 3X^2Y^4 +3X^2 + 3Y^2 - 3X^4 - 3Y^4 -6X^2Y^2 - 1