Adding which terms to 3x2y would result in a monomial? Check all that apply.

3xy
–12x2y
2x2y2
7xy2
–10x2
4x2y
3x3

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.

Learn how to add terms to 3x^2y to form monomials. Understand the rules of combining like terms in algebraic expressions with detailed explanations and examples. Suitable for students in Grades 6-8.

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