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!