Rewrite in simplest terms: 8, left parenthesis, minus, 6, f, minus, 9, right parenthesis, plus, 2, left parenthesis, 9, f, plus, 2, right parenthesis8(−6f−9)+2(9f+2)

To rewrite the expression \( 8(-6f - 9) + 2(9f + 2) \) in its simplest form, we can use the distributive property to eliminate the parentheses and then combine like terms.

1. Distribute \( 8 \) in the first set of parentheses:  
   \( 8 \cdot (-6f) + 8 \cdot (-9) = -48f - 72 \)

2. Distribute \( 2 \) in the second set of parentheses:  
   \( 2 \cdot 9f + 2 \cdot 2 = 18f + 4 \)

3. Combine the results:  
   \( -48f - 72 + 18f + 4 \)

4. Combine like terms (terms with \( f \) and constant terms):  
   \( (-48f + 18f) + (-72 + 4) = -30f - 68 \)

Therefore, the simplified form of the expression is:  
\[
-30f - 68
\]

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would you solve the expression \( 7(3f - 5) - 4(2f + 1) \) in simplest terms?
2. What is the distributive property, and why is it useful in algebra?
3. How can we simplify expressions with multiple variables, such as \( 4x(2y + 3) - 3y(2x + 5) \)?
4. What are like terms, and how do we identify and combine them in an expression?
5. Can you solve \( 5(4f - 7) + 3(2f + 9) \) and explain each step?

**Tip:** Always look for like terms to combine when simplifying algebraic expressions; this helps in reducing the complexity of the equation.

Learn how to simplify the expression 8(-6f - 9) + 2(9f + 2) using the distributive property and combining like terms. Follow a detailed step-by-step solution to reduce the complexity of the algebraic expression. Suitable for high school students studying algebra.

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