Adding Which Terms To 3 X 2 Y 3x^2y 3 X 2 Y Would Result In A Monomial? Check All That Apply.- 3 X Y 3xy 3 X Y - − 12 X 2 Y -12x^2y − 12 X 2 Y - 2 X 2 Y 2 2x^2y^2 2 X 2 Y 2 - 7 X Y 2 7xy^2 7 X Y 2 - − 10 X 2 -10x^2 − 10 X 2 - 4 X 2 Y 4x^2y 4 X 2 Y - 3 X 3 3x^3 3 X 3

Understanding Monomials

A monomial is an algebraic expression that consists of only one term. It is a product of a constant and one or more variables raised to non-negative integer powers. In other words, a monomial is a single term that cannot be simplified further. For example, $3x^2y$ is a monomial because it consists of only one term.

Adding Terms to $3x^2y$

To determine which terms can be added to $3x^2y$ to result in a monomial, we need to consider the properties of monomials. A monomial must have only one term, and the variables in the term must have non-negative integer powers.

Option 1: $3xy$

The term $3xy$ has only one variable, $x$, raised to the power of 1, and the constant is 3. However, the term $3xy$ has a different variable, $y$, which is not present in the original term $3x^2y$. Therefore, adding $3xy$ to $3x^2y$ would result in a binomial, not a monomial.

Option 2: $-12x^2y$

The term $-12x^2y$ has the same variable, $x$, raised to the power of 2, and the same variable, $y$. However, the constant is different, which is -12. Adding $-12x^2y$ to $3x^2y$ would result in a binomial, not a monomial.

Option 3: $2x^2y^2$

The term $2x^2y^2$ has the same variable, $x$, raised to the power of 2, and the same variable, $y$, raised to the power of 2. However, the constant is different, which is 2. Adding $2x^2y^2$ to $3x^2y$ would result in a binomial, not a monomial.

Option 4: $7xy^2$

The term $7xy^2$ has a different variable, $y$, raised to the power of 2, and the constant is 7. Adding $7xy^2$ to $3x^2y$ would result in a binomial, not a monomial.

Option 5: $-10x^2$

The term $-10x^2$ has the same variable, $x$, raised to the power of 2, but the constant is different, which is -10. Adding $-10x^2$ to $3x^2y$ would result in a binomial, not a monomial.

Option 6: $4x^2y$

The term $4x^2y$ has the same variable, $x$, raised to the power of 2, and the same variable, $y$. However, the constant is different, which is 4. Adding $4x^2y$ to $3x^2y$ would result in a binomial, not a monomial.

Option 7: $3x^3$

The term $3x^3$ has the same variable, $x$, but raised to the power of 3, which is different from the original term $3x^2y$. Adding $3x^3$ to $3x^2y$ would result in a binomial, not a monomial.

Conclusion

Based on the analysis above, none of the options can be added to $3x^2y$ to result in a monomial. A monomial must have only one term, and the variables in the term must have non-negative integer powers. Therefore, the correct answer is:

None of the above

However, if we consider the possibility of adding a term that has the same variable, $x$, raised to the power of 2, and the same variable, $y$, but with a different constant, then the correct answer would be:

• $-10x^2$ is not correct, but if we consider the term $10x^2$ (which is not listed), then it would be correct.

Q: What is a monomial?

A monomial is an algebraic expression that consists of only one term. It is a product of a constant and one or more variables raised to non-negative integer powers.

Q: What are the properties of a monomial?

A monomial must have only one term, and the variables in the term must have non-negative integer powers.

Q: Can we add $3xy$ to $3x^2y$ to result in a monomial?

No, adding $3xy$ to $3x^2y$ would result in a binomial, not a monomial. The term $3xy$ has a different variable, $y$, which is not present in the original term $3x^2y$.

Q: Can we add $-12x^2y$ to $3x^2y$ to result in a monomial?

No, adding $-12x^2y$ to $3x^2y$ would result in a binomial, not a monomial. The constant is different, which is -12.

Q: Can we add $2x^2y^2$ to $3x^2y$ to result in a monomial?

No, adding $2x^2y^2$ to $3x^2y$ would result in a binomial, not a monomial. The term $2x^2y^2$ has the same variable, $x$, raised to the power of 2, and the same variable, $y$, raised to the power of 2, but the constant is different, which is 2.

Q: Can we add $7xy^2$ to $3x^2y$ to result in a monomial?

No, adding $7xy^2$ to $3x^2y$ would result in a binomial, not a monomial. The term $7xy^2$ has a different variable, $y$, raised to the power of 2, and the constant is 7.

Q: Can we add $-10x^2$ to $3x^2y$ to result in a monomial?

No, adding $-10x^2$ to $3x^2y$ would result in a binomial, not a monomial. The term $-10x^2$ has the same variable, $x$, raised to the power of 2, but the constant is different, which is -10.

Q: Can we add $4x^2y$ to $3x^2y$ to result in a monomial?

No, adding $4x^2y$ to $3x^2y$ would result in a binomial, not a monomial. The term $4x^2y$ has the same variable, $x$, raised to the power of 2, and the same variable, $y$, but the constant is different, which is 4.

Q: Can we add $3x^3$ to $3x^2y$ to result in a monomial?

No, adding $3x^3$ to $3x^2y$ would result in a binomial, not a monomial. The term $3x^3$ has the same variable, $x$, but raised to the power of 3, which is different from the original term $3x^2y$.

Q: What is the correct answer?

None of the options can be added to $3x^2y$ to result in a monomial.

Q: What is the condition for a term to be added to $3x^2y$ to result in a monomial?

A term can be added to $3x^2y$ to result in a monomial if it has the same variable, $x$, raised to the power of 2, and the same variable, $y$, but with a different constant.

Q: What is an example of a term that can be added to $3x^2y$ to result in a monomial?

An example of a term that can be added to $3x^2y$ to result in a monomial is $10x^2$.