g. \( -x^{2}+(-3 x)^{2}-3 x^{2} \times \frac{a^{2}}{-x} \)

Let's have some fun simplifying this expression step by step! First, let's unpack the expression: 1. The term \( (-3x)^2 \) becomes \( 9x^2 \). 2. Now plugging it back in, we get: \( -x^2 + 9x^2 - 3x^2 \times \frac{a^2}{-x} \). Next, combine the like terms: - Combine \( -x^2 + 9x^2 \) to get \( 8x^2 \). - Now, handle the term \( -3x^2 \times \frac{a^2}{-x} \), which simplifies to \( 3ax^2 \). Now, put everything together: \[ 8x^2 + 3ax^2 = (8 + 3a)x^2 \]. Voila! The expression simplifies to \( (8 + 3a)x^2 \). What a ride, huh? And remember, if you happen to mix up the signs or forget to simplify, don't worry! Just go back and carefully recheck each term—it’ll help you stay on the right track.