To simplify the expression $-10(-5f + 7f + 2) - f$, let's go through it step-by-step:

Step 1: Simplify inside the parentheses

Combine like terms inside the parentheses: $-5f + 7f + 2 = 2f + 2$ So, the expression becomes: $-10(2f + 2) - f$

Step 2: Distribute the $-10$

Now, distribute $-10$ to both terms inside the parentheses: $-10 \cdot 2f + (-10) \cdot 2 = -20f - 20$ Thus, the expression is now: $-20f - 20 - f$

Step 3: Combine like terms

Combine the $f$-terms: $-20f - f = -21f$ So, the final simplified expression is: $-21f - 20$

Final Answer

$-21f - 20$

Would you like further details or have any questions on this process?

Here are 5 additional questions related to simplifying expressions:

1. How do you simplify an expression with multiple variables?
2. What are the steps to distribute a negative sign across terms inside parentheses?
3. How can you factor expressions after simplification?
4. What is the difference between combining like terms and distributing terms?
5. How do coefficients affect terms in polynomial expressions?

Tip: Always combine like terms before distributing to make simplification easier.