C) \( (3+a)^{3} \)

Did you know that the expression \( (3+a)^{3} \) can be expanded using the binomial theorem? This theorem states that \( (x+y)^n \) can be expressed as a sum of terms involving coefficients that count the number of ways to choose \( k \) items from \( n \). So, for \( (3+a)^{3} \), you'd expand it as \( 3^3 + 3 \cdot 3^2 \cdot a + 3 \cdot 3 \cdot a^2 + a^3 \), which simplifies to \( 27 + 27a + 9a^2 + a^3 \). Voila! When simplifying expressions like \( (3+a)^{3} \), a common mistake is forgetting to properly multiply the coefficients and account for each term in the expansion. It's a classic blunder! Also, making sure to keep your variables organized and coefficients clear can help avoid confusion. So take a moment, breathe, and double-check your work—an extra pair of eyes (or your own) can save you from a small slip!