Let's expand the expression \((2x - 3u - 6)(5x + 3u)\) using the distributive property (FOIL method, for binomials).

First, I'll split it into smaller parts:

\[
(2x - 3u - 6)(5x + 3u) = [2x(5x + 3u)] + [-3u(5x + 3u)] + [-6(5x + 3u)]
\]

Now let's multiply each part:

1. \(2x(5x + 3u) = 10x^2 + 6xu\)
2. \(-3u(5x + 3u) = -15xu - 9u^2\)
3. \(-6(5x + 3u) = -30x - 18u\)

Now, combine all the terms:

\[
10x^2 + 6xu - 15xu - 9u^2 - 30x - 18u
\]

Simplify by combining like terms:

\[
10x^2 - 9xu - 9u^2 - 30x - 18u
\]

So, the expanded form of the expression is:

\[
10x^2 - 9xu - 9u^2 - 30x - 18u
\]

Would you like more details on any part of the process? Here are five related questions:

1. How would you factor a similar expression?
2. What are like terms, and how do you combine them?
3. Can you use substitution to solve this equation?
4. How does this expression change if \( u = 0 \)?
5. What happens if you set both variables \( x \) and \( u \) to specific values?

**Tip:** Always combine like terms to simplify the expanded expression and avoid unnecessary complexity.

Learn how to expand the polynomial expression (2x - 3u - 6)(5x + 3u) using the distributive property. This step-by-step solution simplifies the expression, covering key algebraic concepts. Suitable for students in Grades 8-10.

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