To simplify the expression \((b + 3)(3b - 3)\), you can apply the distributive property (also known as FOIL for binomials):

\[
(b + 3)(3b - 3) = b(3b) + b(-3) + 3(3b) + 3(-3)
\]

Now simplify each term:

\[
= 3b^2 - 3b + 9b - 9
\]

Combine like terms:

\[
= 3b^2 + 6b - 9
\]

So, the simplified expression is:

\[
3b^2 + 6b - 9
\]

Would you like more details on any step?

Here are 5 related questions:
1. How would you factor the expression \(3b^2 + 6b - 9\)?
2. What happens if you substitute a specific value for \(b\) in the simplified expression?
3. How does the distributive property work for more complex polynomials?
4. How would this expression change if you had \((b+4)(3b-3)\) instead?
5. Can this expression be solved as part of a quadratic equation?

**Tip**: Always combine like terms carefully to avoid errors when simplifying!

Understand how to simplify the algebraic expression (b+3)(3b-3) by applying the distributive property (FOIL method). This step-by-step solution helps you learn key algebraic concepts, such as polynomial multiplication and combining like terms, suitable for students in Grades 7-9.

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