The given expression is:

$4x^2 + 3xy + 12yz$

Classification:

1. Degree of the expression:

   • The degree of a term is the sum of the exponents of the variables in that term.
     • For $4x^2$, the degree is $2$ (since the exponent of $x$ is 2).
     • For $3xy$, the degree is $1 + 1 = 2$ (since both $x$ and $y$ have an exponent of 1).
     • For $12yz$, the degree is $1 + 1 = 2$ (since both $y$ and $z$ have an exponent of 1).

   Since all the terms have a maximum degree of 2, the overall degree of the expression is 2.

2. Number of terms: There are three terms: $4x^2$, $3xy$, and $12yz$, so it's a trinomial.

Conclusion:

The expression is a 2nd degree trinomial.

Would you like more details or have any questions?

Here are some related questions:

1. How do you classify polynomials based on their degree and number of terms?
2. What is the difference between a monomial, binomial, and trinomial?
3. How do you determine the degree of a polynomial with multiple variables?
4. Can a trinomial have different degrees for each term?
5. How do you add or subtract polynomials with different degrees?

Tip: Always look for the highest degree in the terms to determine the degree of a polynomial.