Question

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

3xy

–12x2y

2x2y2

7xy2

–10x2

4x2y

3x3

Answer 1

Answer:
`-12x^2y\ and\ 4x^2y`

Explanation:

Given monomial:
`3x^2y`, here deg of x is 2 and deg of y is 1

From the options, we have
`-12x^2y\ and\ 4x^2y` polynomials [with deg of x is 2 and deg of y is 1]which are like to the given polynomial.

We know that if we add like monomials, then we get result as mnomila.

Rest of other monomials are unlike to the given monomial, which will result into binomial.

`1)3x^2y+3xy\\2)-12x^2y+3x^y=-9x^2y\\3)2x^2y^2+3x^2y\\4)7x^y+3x^2y\\5)-10x^2+3x^2y\\6)4x^2y+3x^2y=7x^2y\\7)3x^3+3x^2y`

Answer 2

`-12x^(2)y` and
`4x^(2)y`

Explanation:

We are given the term
`3x^(2)y`.

It is known that, 'A monomial is an algebraic expression consisting of one term'.

So, we add the given options to
`3x^(2)y`.

1.
`3x^(2)y+3xy=3xy(x+1)`

2.
`3x^(2)y-12x^(2)y=-9x^(2)y`

3.
`3x^(2)y+2x^(2)y^(2)=x^(2)y(3+2y)`

4.
`3x^(2)y+7xy^(2)=xy(3x+7y)`

5.
`3x^(2)y-10x^(2)=x^(2)(3y-10)`

6.
`3x^(2)y+4x^(2)y=7x^(2)y`

7.
`3x^(2)y+3x^(3)=3x^(2)(y+x)`

As, we can see that only option 2 and 6 results in an expression having one term.

Thus, adding
`-12x^(2)y` and
`4x^(2)y` to
`3x^(2)y` results in a monomial.