 6, left parenthesis, d, minus, 6, f, right parenthesis, minus, 6, f, minus, 3, left parenthesis, minus, 7, f, plus, 8, d, right parenthesis6(d−6f)−6f−3(−7f+8d)

Let's solve the expression:

\[
6(d - 6f) - 6f - 3(-7f + 8d)
\]

### Step-by-step solution:

1. **Distribute** the constants inside the parentheses:
   - For the first term: \( 6(d - 6f) = 6d - 36f \)
   - For the second term: remains as \( -6f \)
   - For the third term: \( -3(-7f + 8d) = 21f - 24d \)

   So the expression becomes:
   \[
   6d - 36f - 6f + 21f - 24d
   \]

2. **Combine like terms**:
   - Combine the \( d \)-terms: \( 6d - 24d = -18d \)
   - Combine the \( f \)-terms: \( -36f - 6f + 21f = -21f \)

So the simplified expression is:
\[
-18d - 21f
\]

### Final answer:
\[
-18d - 21f
\]

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How would the expression change if the signs of the terms were reversed?
2. Can you apply the distributive property to more complex expressions?
3. How do you simplify an expression with three or more variables?
4. How would this expression look if factored?
5. What if instead of \( d \) and \( f \), other variables were used?

**Tip:** Always apply the distributive property before combining like terms when simplifying algebraic expressions!

Learn how to simplify the algebraic expression 6(d−6f)−6f−3(−7f+8d) using the distributive property and combining like terms. This step-by-step guide is perfect for students in Grades 8-10, covering key algebraic concepts and simplification techniques.

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