The expression shown in the image is:

$7(-6f + 1) - 2(3f - 8)$

Let's simplify it step by step.

Step 1: Distribute the constants through the parentheses.

• First, distribute the 7 to the terms inside the first parentheses: $7(-6f + 1) = 7(-6f) + 7(1) = -42f + 7$
• Next, distribute the $-2$ to the terms inside the second parentheses: $-2(3f - 8) = -2(3f) + (-2)(-8) = -6f + 16$

Step 2: Combine like terms.

Now, we combine the like terms from the two expressions: $-42f + 7 - 6f + 16$

Group the $f$ terms together and the constants together: $(-42f - 6f) + (7 + 16) = -48f + 23$

Final Answer:

$-48f + 23$

This is the simplified expression.

Let me know if you would like further details or explanations! Here are a few questions to explore further:

1. How would the result change if the signs inside the parentheses were different?
2. Can you identify other methods to simplify this expression?
3. How do we know when an expression is in its simplest form?
4. Why is it important to distribute negative signs carefully during simplification?
5. What is the significance of combining like terms in algebra?

Tip: Always be mindful of negative signs when distributing across terms to avoid mistakes!