Answer: Algebra tiles can be used to represent algebraic expressions and equations visually. Each tile has a specific value and can be arranged to model different expressions. In your question, you've provided several expressions. I'll break down the representation for each one:
1. **4x + 10:**
- You would have 4 'x' tiles and 10 unit tiles.
2. **(4x + 4)(6x + 6):**
- This represents a product of two binomials. You would use a rectangle to represent this product. You would have four 4x tiles, four 6x tiles, four 4 unit tiles, and six 6 unit tiles.
3. **(2x^2 + 6)(4x + 6):**
- This also represents a product of two binomials. You would use a rectangle to represent this product. You would have two 2x^2 tiles, six 4x tiles, two 2x unit tiles, and six 6 unit tiles.
4. **(2x + 2)(2x + 3):**
- Again, a product of two binomials. You would have two 2x tiles, three 2x tiles, two 2 unit tiles, and three 2 unit tiles.
Remember that these representations help in understanding algebraic expressions visually and can be used for various algebraic operations.