Which is a correct expansion of \( (3 x+2)\left(3 x^{2}+4\right) \) ? A. \( 3 x \cdot 3 x^{2}+3 x \cdot 4+2 \cdot 3 x+2 \cdot 4 \) B. \( 3 x \cdot 3 x^{2}+2 \cdot 3 x^{2}+3 x^{2} \cdot 4+2 \cdot 4 \) c. \( 3 x \cdot 3 x^{2}+3 x \cdot 4+2 \cdot 3 x^{2}+2 \cdot 4 \)

Let's break down the expansion of \( (3 x+2)(3 x^{2}+4) \) correctly. When distributing, you take each term of the first binomial and multiply it by each term of the second binomial. So, we have: 1. \( 3x \cdot 3x^2 \) 2. \( 3x \cdot 4 \) 3. \( 2 \cdot 3x^2 \) 4. \( 2 \cdot 4 \) Now, if we look at the options given: - Option A includes the correct terms but makes a mistake with the arrangement and duplicates. - Option B incorrectly includes \( 3x^2 \) (can you find it?). - Option C, however, showcases all the correct distributions perfectly! This means option C is your winner! Happy expanding, mathematician! So, looking closer at polynomial expansions in math is essential. A common pitfall is omitting terms or not aligning like terms correctly. Always double-check each term before finalizing your answer! For further exploration, check out algebra textbooks or online resources that detail polynomial multiplication and factorization. They often have practice problems and explanations that could spice up your algebra skills!