https://file.aiquickdraw.com/mathbot/file/1726481533200kxtkr5t3.jpg

The expression in the image contains three terms: 

\[
7m^2n, \ 28mn^2, \ 98mn
\]

Let's find the greatest common factor (GCF) of these three terms.

1. **Numerical GCF**: The GCF of 7, 28, and 98 is 7.
2. **Variable GCF**: 
   - For \( m \), the lowest power of \( m \) in the terms is \( m^1 \).
   - For \( n \), the lowest power of \( n \) in the terms is \( n^1 \).

Therefore, the GCF of the three terms is:

\[
7mn
\]

Now, we can factor out \( 7mn \) from each term:

\[
7m^2n = 7mn \cdot m
\]
\[
28mn^2 = 7mn \cdot 4n
\]
\[
98mn = 7mn \cdot 14
\]

So the factored form of the expression is:

\[
7mn(m + 4n + 14)
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions to expand on this topic:

1. How do you find the greatest common factor of more complex polynomials?
2. Can this expression be further simplified or factored?
3. What happens when there are more variables involved in the terms?
4. How does factoring help in solving polynomial equations?
5. Can you apply the distributive property to expand the factored form?

**Tip:** Always check each term's coefficients and variables individually when finding the GCF!

Learn how to factor the algebraic expression containing the terms 7m^2n, 28mn^2, and 98mn. This problem focuses on finding the greatest common factor and using the distributive property. Suitable for students in Grades 8-10.

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