what is the polynomial classification and terminolofy of (3Xsquared-2XY-2Xsquared+3XY=Ycubed)?

Answer 1

conic equation

Answer 2

If we use ^ to mean 'to the power of' then you've got a polynomial: 3x^2 - 2xy - 2x^2 + 3xy = y (presuming there was nothing missing at the end there).
Simplifying by adding like terms together, we could write:
x^2 + xy - y = 0

Polynomials tend to be classified by the number of 'terms' in the expression, in this case 3: x^2 is one term, xy is another and -y is another.

So it is a polynomial with 3 terms, or a 'trinomial'.

We would also describe the expression by the 'degree' of the polynomial. The degree of a term is the sum of the exponents of it's variables. Our variables here are x and y so the degrees of the first and second terms, x^2 and xy, are both 2. The degree of the third term, y, is just 1.
The degree of the polynomial is the highest degree of it's terms. In this case 2 is the highest degree.

So, it's a second degree polynomial with three terms, or we could say, a 'quadratic trinomial' (quadratic just means 'second degree').

We would tend to write the expression with it's terms in descending order of degree, which looks like this:

x^2 + xy - y = 0

Hope that answers your question!