Question

Adding which terms to 3x2y would result in a monomial? Check all that apply.
3xy
–12x2y
2x2y2
7xy2
–10x2
4x2y
3x3

Answer 1

Only the terms containing the variables x²y are "like" terms:
  -12x²y
  4x²y

Answer 2

Answer:

The answers are $-12*x^2*y$ , $4*x^2*y$

Step-by-step explanation:

Firstly, in Algebra a monomial is an expression that contains one term, like 10xz. Monomials include: numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together. Any number, all by itself, is a monomial, like 10 or 3,400. A monomial can also be a variable, like q or p. It can also be a combination of these, like 101a or 13qxz.

The procedure to add monomials is:

1. The first thing you need to do is to check to see if your monomials are like terms. You ask yourself, are the variables exactly the same?
2. If the answer is "Yes", that means you can go ahead and add them together.
3. You leave the variables as they are and you add up the coefficients.

So, in this case, the variables of $3*x^2*y$  is   $x^2*y$

Then, you check which option has the same variables. The valid options are:

$-12*x^2*y\\4*x^2*y$

Finally,

$3*x^2*y+(-12*x^2*y)=(3-12)*x^2*y=-9*x^2*y\\3*x^2*y+4*x^2*y=(3+4)*x^2*y=7*x^2*y$