Question

adding which terms to $3x^2y$ would result in a monomial? check all that apply.
$3xy$
$-12x^2y$
$2x^2y^2$
$7xy^2$
$-10x^2$
$4x^2y$
$3x^3$

Explanation:

Step1: Identify like terms

Like terms have identical variables with same exponents. The given term is $3x^2y$, so we look for terms with $x^2y$.

Step2: Check each option

• $3xy$: Variables $x^1y^1$ (not like term)
• $-12x^2y$: Variables $x^2y^1$ (like term)
• $2x^2y^2$: Variables $x^2y^2$ (not like term)
• $7xy^2$: Variables $x^1y^2$ (not like term)
• $-10x^2$: Variables $x^2$ (not like term)
• $4x^2y$: Variables $x^2y^1$ (like term)
• $3x^3$: Variables $x^3$ (not like term)

Step3: Verify sum is monomial

Adding like terms gives a single term (monomial):
$3x^2y + (-12x^2y) = -9x^2y$
$3x^2y + 4x^2y = 7x^2y$

Answer:

• $-12x^2y$
• $4x^2y$