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Let's solve the given expression step by step by factoring through grouping. The expression is:

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

### Step 1: Group the terms
We can group the terms as follows:
\[
(b^2 + 3b) - (3b + 9)
\]

### Step 2: Factor out the greatest common factor (GCF) from each group
- In the first group \(b^2 + 3b\), the GCF is \(b\):
  \[
  b(b + 3)
  \]
- In the second group \(-3b - 9\), the GCF is \(-3\):
  \[
  -3(b + 3)
  \]

### Step 3: Factor by grouping
Now we have:
\[
b(b + 3) - 3(b + 3)
\]

Notice that \((b + 3)\) is common in both terms. So, we can factor this out:
\[
(b - 3)(b + 3)
\]

### Final Answer:
The factored form of the expression is:
\[
(b - 3)(b + 3)
\]

Let me know if you'd like more details, or if you have any other questions!

Here are 5 related questions to expand your understanding:
1. What happens when you expand the factored form \((b - 3)(b + 3)\)?
2. How would you factor \(b^2 + 6b + 9\)?
3. Can you apply grouping to factor other types of quadratic expressions?
4. What is the general process of factoring by grouping for four-term polynomials?
5. How do you recognize which terms to group when factoring?

**Tip:** Always look for common factors within grouped terms before factoring completely!

Learn how to factor the quadratic expression b^2 + 3b - 3b - 9 by grouping. This solution covers key algebraic concepts such as factoring by grouping and the difference of squares theorem. Suitable for students in Grades 8-10.

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