Marianne claims that $m^2$ and $3 m^2$ are the like terms in the expression $m^2+2 x-x+3 m^2+2$. Did Marianne identify the correct like terms?

AYes, Marianne correctly identified the like terms.
BNo, she is missing the like terms $2 x$ and 2.
CNo, she is missing the like terms $2 x$ and $-x$.
DNo, $m^2$ and $3 m^2$ are not like terms because the coefficients are different.

Question

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03-11-2026
Mathematics

Answered

Marianne claims that $m^2$ and $3 m^2$ are the like terms in the expression $m^2+2 x-x+3 m^2+2$. Did Marianne identify the correct like terms?

AYes, Marianne correctly identified the like terms.
BNo, she is missing the like terms $2 x$ and 2.
CNo, she is missing the like terms $2 x$ and $-x$.
DNo, $m^2$ and $3 m^2$ are not like terms because the coefficients are different.

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T20:50:41-05:00

The expression given is $m^2 + 2x - x + 3m^2 + 2$.
Like terms are defined by having identical variable parts and exponents.
The term $m^2$ and $3m^2$ are like terms, but the terms $2x$ and $-x$ are also like terms.
Marianne missed the pair $2x$ and $-x$, so the correct answer is $\boxed{c}$.

Explanation

Understanding Like Terms

We are given the algebraic expression $m^2 + 2x - x + 3m^2 + 2$. Like terms are defined as terms within an algebraic expression that have the same variables raised to the same powers. We need to identify all sets of like terms within this expression and evaluate Marianne's claim that $m^2$ and $3m^2$ are the only like terms.

Identifying Like Terms in the Expression

Let's list all the terms in the expression: $m^2$, $2x$, $-x$, $3m^2$, and $2$.

Now, let's group them by their variable parts:

For the variable $m$: The terms are $m^2$ and $3m^2$. Both have the variable $m$ raised to the power of 2, so they are like terms.
For the variable $x$: The terms are $2x$ and $-x$. Both have the variable $x$ raised to the power of 1, so they are like terms.
For the constant term: The term is $2$. There are no other constant terms in the expression, so it has no like terms.

Evaluating Marianne's Claim

Marianne identified the pair $m^2$ and $3m^2$. While this pair is indeed composed of like terms, she failed to identify the other pair of like terms, which are $2x$ and $-x$. Since she missed a pair, her statement that these are "the" like terms is incomplete. Comparing this to the provided options, option (c) correctly states that she missed the like terms $2x$ and $-x$.

Conclusion

Based on the analysis, the correct option is (c). Marianne correctly identified one pair of like terms but missed another. The final answer is $\boxed{c}$.

Examples

Understanding like terms is essential for simplifying algebraic expressions, much like organizing items into categories. If you were organizing inventory in a warehouse, you would group items of the same type together, such as all boxes of size $A$ or all boxes of size $B$. In algebra, combining like terms $2x + 3x = 5x$ allows you to consolidate information, making equations easier to solve and interpret. This fundamental skill is the building block for all higher-level algebra and problem-solving.