Prove that $\sin^4(x)\cos^2(x) + \sin^2(x)\cos^4(x) - \sin^2(x)\cos^2(x)=0.$ Using the following expression:
$$\sin^4(x)\cos^2(x) + \sin^2(x)\cos^4(x) - \sin^2(x)\cos^2(x).$$
The above expression is supposed to evaluate to zero, but how?

Let $\sin^2(x) = y$.
Note that $\cos^2(x) = 1-\sin^2(x) = 1- y$.
Your expression now becomes:
$$y^2(1-y) + y(1-y)^2 - y(1-y) = y(1-y)(y + (1-y) - 1) = y(1-y)(0) = 0.$$
