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The expression given is:

\[
-7n(5n + 6)
\]

We will expand this expression using the distributive property, which states that \( a(b + c) = ab + ac \).

1. Distribute \( -7n \) to each term inside the parentheses:
   \[
   -7n \times 5n = -35n^2
   \]
   \[
   -7n \times 6 = -42n
   \]

So, the expanded expression is:
\[
-35n^2 - 42n
\]

Now, let's compare this result to the given options:

- A) \( -12n + 28 \)
- B) \( -35n^2 - 42n \)
- C) \( -6n + 4 \)
- D) \( 2n^2 - 4n \)

The correct answer is **B**.

Would you like more details or have any questions about this process? 

Here are 5 related questions to expand your understanding:
1. How does the distributive property work for multiplying variables and constants?
2. What is the importance of recognizing similar terms in algebraic expressions?
3. Can you explain how \( n^2 \) changes the degree of a polynomial?
4. How would this problem change if there was an addition or subtraction sign outside the parentheses?
5. What if the coefficient inside the parentheses was negative instead of positive?

**Tip**: Always distribute each term carefully when working with multiple variables or constants to avoid mistakes.

Expand the algebraic expression: -7n(5n + 6) and select the correct option from A) -12n + 28, B) -35n^2 - 42n, C) -6n + 4, D) 2n^2 - 4n.

Learn how to expand the algebraic expression -7n(5n + 6) using the distributive property. This problem focuses on key algebraic concepts and polynomial expansion, suitable for students in Grades 7-9.

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