To solve the expression \(6xy + 4x - 2yx + 5\) step by step, we'll start by simplifying it.

### Step 1: Combine like terms
First, notice that \(6xy\) and \(-2yx\) are like terms because they both involve the product of \(x\) and \(y\). Since multiplication is commutative, \(xy\) is the same as \(yx\).

So, combine these two terms:
\[
6xy - 2yx = 6xy - 2xy = 4xy
\]

### Step 2: Rewrite the expression
Now, rewrite the expression with the simplified terms:
\[
4xy + 4x + 5
\]

### Step 3: Factor, if possible
Check if the expression can be factored further. In this case, the terms \(4xy\), \(4x\), and \(5\) don't share a common factor, so the expression can't be factored further.

### Final Answer:
The simplified expression is:
\[
4xy + 4x + 5
\]

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How do you factor expressions involving multiple variables?
2. What is the difference between like terms and unlike terms?
3. How can you check if an expression is fully simplified?
4. What are the properties of multiplication that help in simplifying expressions?
5. How do you solve an equation once you have a simplified expression?

**Tip:** Always double-check for like terms in algebraic expressions, as combining them is key to simplification.

Discover how to simplify the algebraic expression 6xy + 4x - 2yx + 5 with a step-by-step guide. This solution explores combining like terms using the commutative property and offers a simplified expression. Ideal for middle school students (Grades 6-8).

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