minus, 4, left parenthesis, 8, f, plus, g, right parenthesis, plus, 9, g, minus, 5, left parenthesis, minus, 2, g, plus, 6, f, right parenthesis−4(8f+g)+9g−5(−2g+6f)

Answer 1

To simplify the given expression \( -4(8f+g) + 9g - 5(-2g+6f) \), we will follow the order of operations, distributing terms where necessary.

1. Distribute the \(-4\) across \( (8f + g) \): \[ -4(8f + g) = -32f - 4g \]

2. Distribute the \(-5\) across \( (-2g + 6f) \): \[ -5(-2g + 6f) = 10g - 30f \]

Now substituting these results back into the expression: \[ -32f - 4g + 9g + 10g - 30f \]

3. Now we can combine like terms:
   • For the \(f\) terms: \(-32f - 30f = -62f\)
   • For the \(g\) terms: \(-4g + 9g + 10g = 15g\)

Putting it all together, the simplified expression is: \[ -62f + 15g \]

Thus, the final answer is: \[ -62f + 15g \]