adding which terms to $3x^{2}y$ would result in a monomial? check all that apply.\n$3xy$\n$-12x^{2}y$\n$2x^{2…

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

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

Answer

Explanation:

Step1: Recall like - terms concept

Like - terms can be combined to form a monomial. Like terms have the same variables raised to the same powers. The given term is $3x^{2}y$.

Step2: Analyze each option

  • For $3xy$, the power of $x$ is 1 instead of 2, not like - terms.
  • For $- 12x^{2}y$, it has the same variables $x$ and $y$ with powers 2 and 1 respectively as in $3x^{2}y$. $3x^{2}y+( - 12x^{2}y)=(3 - 12)x^{2}y=-9x^{2}y$, a monomial.
  • For $2x^{2}y^{2}$, the power of $y$ is 2 instead of 1, not like - terms.
  • For $7xy^{2}$, the power of $x$ is 1 instead of 2, not like - terms.
  • For $-10x^{2}$, it has no $y$ variable, not like - terms.
  • For $4x^{2}y$, it has the same variables $x$ and $y$ with powers 2 and 1 respectively as in $3x^{2}y$. $3x^{2}y + 4x^{2}y=(3 + 4)x^{2}y = 7x^{2}y$, a monomial.
  • For $3x^{3}$, it has no $y$ variable and the power of $x$ is 3 instead of 2, not like - terms.

Answer:

-12x^{2}y, 4x^{2}y