Let's simplify the expression:

Given:  
\[ 8x^2y + 2x - 8xy + 2 \]

1. **Group like terms:**
   - \( 8x^2y \) (there are no other terms with \( x^2y \))
   - \( 2x \) and \( -8xy \)
   - \( 2 \) (constant)

So the expression is:
\[ 8x^2y + (2x - 8xy) + 2 \]

2. **Factor common terms where possible:**
   - In \( 2x - 8xy \), we can factor out \( 2x \):
   \[ 2x(1 - 4y) \]

Thus, the simplified expression is:
\[ 8x^2y + 2x(1 - 4y) + 2 \]

This is the simplest form of the given expression.

Would you like further details on any part of this?

### Related questions:
1. How do you factor more complex expressions with multiple variables?
2. How does grouping terms help in simplifying expressions?
3. Can you explain the process of factoring in algebra?
4. What are the rules for distributing terms across parentheses?
5. How does factoring simplify solving equations?

### Tip:
When simplifying expressions, always check for common factors to make the process more efficient.

Simplify the expression 8x^2y + 2x - 8xy + 2 by grouping like terms and factoring. This algebraic problem involves the distributive property and factoring common terms, making it suitable for students in Grades 8-10.

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