The given expression is:

\[
4y^2x - 4y^2b + 3bm - 3ymx
\]

There aren't any obvious like terms to combine right away, but let's break it down and see if we can simplify or factor anything further.

### Group the terms for better clarity:
\[
(4y^2x - 4y^2b) + (3bm - 3ymx)
\]

- The first two terms \(4y^2x - 4y^2b\) have a common factor of \(4y^2\), so we can factor that out:
\[
4y^2(x - b)
\]

- The last two terms \(3bm - 3ymx\) also have a common factor of \(3m\), so we can factor that out:
\[
3m(b - yx)
\]

### The expression now becomes:
\[
4y^2(x - b) + 3m(b - yx)
\]

This is the simplified version of the given expression.

Would you like to further explore this or have any other questions?

Here are five questions related to this:

1. How do you factor out common terms in expressions?
2. What are like terms, and how can you identify them?
3. How can you apply the distributive property when factoring?
4. What is the difference between factoring and simplifying?
5. How can factoring help in solving equations?

**Tip**: When simplifying expressions, always check for common factors to make the process easier.

Learn how to factor and simplify the algebraic expression 4y^2x - 4y^2b + 3bm - 3ymx step-by-step. This guide covers key algebraic concepts, including factoring common terms and applying the distributive property, ideal for students in Grades 8-10.

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