Final answer:
The expression 3y^2y^2 - 2xy simplifies to 3y^4 - 2xy, making it a binomial since it has two terms. Polynomials are classified by their number of terms, and the given expression falls into the binomial category.
Step-by-step explanation:
The expression given is 3y^2y^2 - 2xy. To classify the polynomial according to its number of terms, we need to simplify the expression first. Upon simplifying, we find that the expression actually represents 3y^4 - 2xy. This expression consists of two terms, therefore classifying it as a binomial.
Recall that a polynomial is an expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are classified based on the number of terms they have: monomials (one term), binomials (two terms), trinomials (three terms), and so on.
In the context of the solution of quadratic equations, it's important to note that while polynomials can be of any order (first, second, etc.), quadratic functions (second-order polynomials) specifically have a variable raised to the second power as their highest exponent.