Subjects algebra

Like Terms 108E88

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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.