https://file.aiquickdraw.com/mathbot/file/1726449329159nkh9tyrt.jpg

The expression given in the image is \(12x^4y^3 + 18x^3y^4\). To factor it completely, let's follow these steps:

1. **Factor out the GCF (Greatest Common Factor):**
   - The GCF of the coefficients 12 and 18 is 6.
   - For the variables, the smallest power of \(x\) is \(x^3\), and the smallest power of \(y\) is \(y^3\).
   
   So, the GCF is \(6x^3y^3\).
   
   Now, factor out the GCF from the original expression:

   \[
   12x^4y^3 + 18x^3y^4 = 6x^3y^3(2x + 3y)
   \]

2. **Choose the correct options from the boxes:**
   - The left box should be \(6x^3y^3\) (the GCF).
   - The right box should be \(2x + 3y\) (the remaining terms after factoring out the GCF).

Thus, the correct choices in the image are:
- For the first part: \(6x^3y^3\) (check that box).
- For the second part: \(2x + 3y\) (check the boxes for \(2x\) and \(3y\)).

Let me know if you would like further clarification or details!

Here are 5 follow-up questions related to factoring expressions:
1. What is the GCF of \(24x^5y^2\) and \(36x^3y^3\)?
2. How do you factor a quadratic expression like \(x^2 - 5x + 6\)?
3. Can every polynomial be factored completely?
4. What is the difference between factoring by grouping and factoring using the GCF?
5. How would you factor a cubic expression like \(x^3 - 27\)?

**Tip:** When factoring, always start by looking for the greatest common factor (GCF) before trying other methods like grouping or special patterns!

Factor the expression 12x^4y^3 + 18x^3y^4 completely.

Learn how to factor the expression 12x^4y^3 + 18x^3y^4 completely by factoring out the GCF. This problem explains the steps involved in identifying the greatest common factor (6x^3y^3) and using the distributive property to simplify the expression to 6x^3y^3(2x + 3y). Suitable for students in Grades 8-10.

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