fully factorise this expression -9xyz-45x2y2z

Let's fully factorize the expression:

\[
-9xyz - 45x^2y^2z
\]

### Step-by-step Factorization:

1. **Find the greatest common factor (GCF):**
   - For the constants: GCF of \(9\) and \(45\) is \(9\).
   - For the variables: The common variables between the terms are \(x\), \(y\), and \(z\), so the GCF is \(xyz\).

Thus, the GCF of the entire expression is \(-9xyz\).

2. **Factor out the GCF:**
   Now, divide each term by \(-9xyz\):

   \[
   -9xyz \left(\frac{-9xyz}{-9xyz} + \frac{-45x^2y^2z}{-9xyz}\right)
   \]

   This simplifies to:

   \[
   -9xyz(1 + 5xy)
   \]

### Final Factorized Form:

\[
-9xyz(1 + 5xy)
\]

Would you like more details on this or have any questions?

Here are 5 related questions:
1. How do you determine the GCF of variables in an expression?
2. What is the process of factoring trinomials?
3. How do you factor expressions with negative coefficients?
4. How can factoring help in solving equations?
5. What are some techniques to factor quadratic expressions?

**Tip:** Always check if you can factor out a negative sign to simplify your expression further.

Learn how to fully factorize the algebraic expression -9xyz - 45x^2y^2z using the GCF method. Follow this step-by-step guide to simplify the expression by factoring out the greatest common factor. Suitable for students in Grades 7-9, covering essential algebra concepts.

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