The given expression is:

\[ 18bx^2 + 18bx - 20b \]

To factor this expression, we can start by factoring out the greatest common factor (GCF) from all the terms. The GCF here is \(2b\), as \(2b\) is the largest term that can be factored from each part of the expression.

So, let's factor out \(2b\):

\[
18bx^2 + 18bx - 20b = 2b(9x^2 + 9x - 10)
\]

Now, we have the expression in a factored form:

\[
2b(9x^2 + 9x - 10)
\]

The quadratic expression inside the parentheses \(9x^2 + 9x - 10\) could be factored further, but since it's not easily factorable using integers, we typically leave it in this form unless you are looking for a more complex factoring involving radicals.

Would you like to factor further using more advanced methods, or do you have any other questions?

### Related Questions:
1. How would you apply the quadratic formula to solve \(9x^2 + 9x - 10 = 0\)?
2. What are the roots of the quadratic equation \(9x^2 + 9x - 10 = 0\)?
3. Can you complete the square for the quadratic expression \(9x^2 + 9x - 10\)?
4. How would this expression change if \(b = 0\)?
5. How do you factor quadratic expressions in general?

**Tip:** Always check for the greatest common factor first when factoring algebraic expressions. This simplifies the problem and makes further factoring easier.

Learn how to factor the expression 18bx^2 + 18bx - 20b using the greatest common factor (GCF) method. This problem covers key algebraic concepts such as factoring and GCF. Suitable for students in Grades 7-9.

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