https://file.aiquickdraw.com/mathbot/file/1728604102390qcnb9sw0.jpg

Let's factor the given expression: 

\[
18u x^4 y^9 + 30u^8 x^7
\]

### Step 1: Identify the Greatest Common Factor (GCF)
Look for common factors in both terms. The first term is \(18u x^4 y^9\) and the second term is \(30u^8 x^7\).

- **Numerical coefficient GCF:** The GCF of 18 and 30 is 6.
- **Variable \(u\):** The lowest power of \(u\) is \(u^1\) (since the first term has \(u^1\) and the second term has \(u^8\)).
- **Variable \(x\):** The lowest power of \(x\) is \(x^4\) (since the first term has \(x^4\) and the second term has \(x^7\)).
- **Variable \(y\):** The first term has \(y^9\), but the second term has no \(y\), so there is no common factor involving \(y\).

Thus, the GCF is:
\[
6u x^4
\]

### Step 2: Factor out the GCF
Now, factor out \(6u x^4\) from both terms.

\[
18u x^4 y^9 + 30u^8 x^7 = 6u x^4 (3y^9 + 5u^7 x^3)
\]

### Final Factored Form:
\[
6u x^4 (3y^9 + 5u^7 x^3)
\]

Let me know if you want any further clarifications or additional details.

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### Related questions:
1. How do you factor expressions with multiple variables?
2. What is the method for finding the greatest common factor of terms with both coefficients and variables?
3. How do powers of variables affect the factoring process?
4. What is the difference between factoring out variables and factoring numbers?
5. How does factoring help simplify polynomial expressions?

### Tip:
Always start by finding the greatest common factor for both the coefficients and variables separately when factoring polynomial expressions.

Factor the following expression: 18u x^4 y^9 + 30u^8 x^7

Learn how to factor the polynomial expression 18u x^4 y^9 + 30u^8 x^7 by finding the greatest common factor (GCF). This detailed solution includes identifying common factors in coefficients and variables, making it suitable for students in Grades 8-10 studying Algebra.

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