3𝑥𝑦2 − 4𝑧 + 5𝑦2𝑥 + 3𝑧 − 5𝑥𝑦z

The expression you've provided is:

\[
3xy^2 - 4z + 5y^2x + 3z - 5xyz
\]

Let's simplify this expression by combining like terms:

1. **Combine the \( xy^2 \) terms**:  
   - \( 3xy^2 \) and \( 5y^2x \) are like terms (since \( xy^2 \) and \( y^2x \) are the same due to the commutative property of multiplication).  
   - Adding these gives \( 3xy^2 + 5xy^2 = 8xy^2 \).

2. **Combine the \( z \) terms**:  
   - \( -4z \) and \( 3z \) are like terms.  
   - Adding these gives \( -4z + 3z = -z \).

3. **The \( -5xyz \) term** doesn't have any like terms, so it stays as is.

So, the simplified expression is:

\[
8xy^2 - z - 5xyz
\]

Would you like more details on any specific part of this process or have any further questions?

### Related Questions:
1. How do you combine like terms in algebraic expressions?
2. What is the commutative property of multiplication?
3. How do you factor out common terms in an expression?
4. How do you handle expressions with multiple variables?
5. What are the steps to simplify polynomial expressions?
6. Can you explain the distributive property of multiplication over addition?
7. How do you identify like terms in an expression?
8. What is the difference between an equation and an expression?

### Tip:
Always group and simplify like terms in algebraic expressions to make calculations easier and more manageable.

Learn how to simplify the algebraic expression 3xy^2 - 4z + 5y^2x + 3z - 5xyz step-by-step. This problem covers algebraic concepts such as polynomials and combining like terms. Suitable for students in Grades 7-9.

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