Please explain how you got this form '10xyz ax - (x^2)z ay + 10y(z^2) az -20'?

and how you get 10yz +20yz

If you are trying to get the gradient of V(x,y,z) you will need to express the gradient in the direction of x, the direction of y and the direction of z.

Thus you should be looking at how you might express this gradient as a vector with partial derivatives.