A monomial is an algebraic expression consisting of a single term. To determine which terms can be added to $3x^2y$ to result in a monomial, we need to ensure the terms have the same variable components with the same exponents.

Given the term $3x^2y$, we are looking for terms that also have $x^2y$.

Let's check each term:

1. $3xy$ - Not a monomial with $3x^2y$ (different exponents for $x$)
2. $-12x^2y$ - This can be combined with $3x^2y$ to form a monomial.
3. $2x^2y^2$ - Not a monomial with $3x^2y$ (different exponents for $y$)
4. $7xy^2$ - Not a monomial with $3x^2y$ (different exponents for both $x$ and $y$)
5. $-10x^2$ - Not a monomial with $3x^2y$ (missing $y$)
6. $4x^2y$ - This can be combined with $3x^2y$ to form a monomial.
7. $3x^3$ - Not a monomial with $3x^2y$ (different exponents for $x$ and missing $y$)

Thus, the terms that can be added to $3x^2y$ to result in a monomial are:

• $-12x^2y$
• $4x^2y$

Would you like more details or have any questions?

Here are 5 more questions for you to explore:

1. What is the sum of $3x^2y$ and $-12x^2y$?
2. How do you multiply two monomials together?
3. What is the degree of the monomial $4x^2y$?
4. How do you simplify the expression $3x^2y + 4x^2y$?
5. What are the coefficients in the monomial $-12x^2y$?

Tip: When combining like terms in algebra, always ensure the variables and their exponents match exactly.