Case context: Like terms have the same variable(s) raised to the same exponent(s). Only like terms can be added or subtracted, by combining their coefficients.

Question: Simplify $25y^2 + 15y^2 + 3v^2$. Explain which terms can combine and why.

Sample answer: $25y^2$ and $15y^2$ are like terms because they both have $y^2$. Add their coefficients: $25y^2 + 15y^2 = 40y^2$. The term $3v^2$ has a different variable, $v$, so it cannot combine with the $y^2$ terms. Final answer: $40y^2 + 3v^2$.

Key points:

• Like terms must share the same variable and exponent
• $25y^2 + 15y^2 = 40y^2$
• $3v^2$ has a different variable, so it cannot combine
• Final simplified expression is $40y^2 + 3v^2$

Rubric: Full credit: correctly identifies $25y^2$ and $15y^2$ as like terms, combines them to $40y^2$, and explains why $3v^2$ stays separate. Partial credit: combines the like terms but gives a weak or missing explanation for $3v^2$. No credit: incorrect combination or no explanation.