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.