Rewrite in simplest terms: \( -4(8 f+g)+9 g-5(-2 g+6 f) \)

Let’s break this down step by step! First, start by distributing the terms: 1. Distributing \( -4 \) gives: \[ -4 \times 8f = -32f \quad \text{and} \quad -4 \times g = -4g \] So, \( -4(8f + g) = -32f - 4g \). 2. For the \( 9g \): \[ 9g \text{ stays as it is.} \] 3. Now distribute \( -5 \) in \( -5(-2g + 6f) \): \[ -5 \times -2g = 10g \quad \text{and} \quad -5 \times 6f = -30f \] So, \( -5(-2g + 6f) = 10g - 30f \). Now combine all these together: \[ -32f - 4g + 9g + 10g - 30f \] Next, combine like terms: - For \( f \) terms: \(-32f - 30f = -62f\) - For \( g \) terms: \(-4g + 9g + 10g = 15g\) So, putting it all together, we get: \[ \boxed{-62f + 15g} \]