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The given expression is:

\[
4ac - 6ab - 6c^2 + 9bc
\]

Let's try to simplify or factor this expression by grouping like terms if possible. 

The terms are:
- \(4ac\)
- \(-6ab\)
- \(-6c^2\)
- \(9bc\)

We can factor out common factors from some of the terms:

1. From the first two terms, \(4ac - 6ab\), we can factor out \(2a\), giving:
   \[
   2a(2c - 3b)
   \]
   
2. From the last two terms, \(-6c^2 + 9bc\), we can factor out \(-3c\), giving:
   \[
   -3c(2c - 3b)
   \]

Now the expression becomes:
\[
2a(2c - 3b) - 3c(2c - 3b)
\]

Since both groups share the common factor \(2c - 3b\), we can factor it out:
\[
(2a - 3c)(2c - 3b)
\]

Thus, the factored form of the expression is:
\[
(2a - 3c)(2c - 3b)
\]

Would you like further explanation or details on this? 

Here are 5 related questions you can explore:
1. How do you identify common factors in polynomials?
2. What is the difference between factoring by grouping and factoring trinomials?
3. How do you check if a factored expression is correct?
4. Can all polynomials be factored?
5. How do the distributive and associative properties help in factoring?

**Tip:** Always check your factored expression by expanding it back to its original form to ensure accuracy.

Learn how to factor the algebraic expression 4ac - 6ab - 6c^2 + 9bc using the grouping method. This example illustrates important algebraic concepts, including factoring polynomials and recognizing common factors. Suitable for students in Grades 9-12.

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