https://file.aiquickdraw.com/mathbot/file/17259631091111ade4wil.jpg

The expression in the image is:

\[
3mn^3p - 3mn^4 + 4m^2n^3 - 4m^2n^2p
\]

Let's factor this expression step by step.

### Step 1: Group the terms

We can group the terms in pairs to make factoring easier:

\[
(3mn^3p - 3mn^4) + (4m^2n^3 - 4m^2n^2p)
\]

### Step 2: Factor out the common factors in each group

1. From the first group \((3mn^3p - 3mn^4)\), we can factor out \(3mn^3\):

   \[
   3mn^3(p - n)
   \]

2. From the second group \((4m^2n^3 - 4m^2n^2p)\), we can factor out \(4m^2n^2\):

   \[
   4m^2n^2(n - p)
   \]

### Step 3: Rearrange the second factor to match the signs

Notice that \((n - p)\) can be rewritten as \(-(p - n)\). Therefore, the second factor can be rewritten as:

\[
4m^2n^2(-1)(p - n) = -4m^2n^2(p - n)
\]

Now, both groups have a common factor of \((p - n)\):

\[
3mn^3(p - n) - 4m^2n^2(p - n)
\]

### Step 4: Factor out the common factor \((p - n)\):

\[
(p - n)(3mn^3 - 4m^2n^2)
\]

So the fully factored form of the expression is:

\[
(p - n)(3mn^3 - 4m^2n^2)
\]

Would you like further details on any of these steps, or do you have any questions?

Here are 5 related questions you might find helpful:
1. How do you factor expressions with more variables?
2. What are common factoring techniques for polynomials?
3. How can you identify common factors in polynomial expressions?
4. How can factoring be used to simplify equations?
5. What are other methods to factor complex expressions?

**Tip:** Always check if each term of the polynomial has a common factor that can be factored out to simplify the expression further.

Factor the expression 3mn^3p - 3mn^4 + 4m^2n^3 - 4m^2n^2p.

Learn how to factor the polynomial expression 3mn^3p - 3mn^4 + 4m^2n^3 - 4m^2n^2p using grouping and the distributive property. Step-by-step guidance provided for students in Grades 9-10.

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