1. The problem asks which expression correctly labels the like terms in the algebraic expression $-14m - 3n + 5 + 4n - 22 + 3n + 6m^2$.
2. Like terms are terms that have the same variable raised to the same power. Constants (numbers without variables) are also like terms with each other.
3. Identify like terms:
- Terms with $m$: $-14m$
- Terms with $n$: $-3n$, $4n$, $3n$
- Constant terms: $5$, $-22$
- Term with $m^2$: $6m^2$
4. Check each expression's grouping:
- Expression A groups $-14m$ and $6m^2$ (yellow ellipses), $-3n$, $4n$, $3n$ (orange rounded rectangles), and $5$, $-22$ (blue rounded rectangles).
- Expression B groups $-14m$, $-3n$, $-22$ (orange rounded rectangles) together, which mixes different variables and constants incorrectly.
- Expression C groups $-14m$ and $6m^2$ (yellow ellipses), $-3n$, $4n$, $3n$ (orange rounded rectangles), $5$, $-22$ (blue rounded rectangles), and also $6m^2$ in a green pentagonal shape, which is inconsistent.
- Expression D groups $-14m$, $-3n$, $4n$, $3n$ (orange rounded rectangles), $5$, $-22$ (blue rounded rectangles), and $6m^2$ (green pentagonal shape), correctly separating terms by their variables and constants.
5. Therefore, Expression D correctly labels the like terms.
**Final answer:** Expression D correctly labels the like terms.
Like Terms 108E88
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.