Question

Use algebra tiles to find (4x+4)–(2x+2).
x
x
x
x
1
1
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1
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x
x
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Combine like terms. For example, write 3 instead of 1 + 1 + 1.

Answer 1

To simplify the expression \((4x + 4) - (2x + 2)\) using algebra tiles and combining like terms, follow these steps:

1. **Representation with Algebra Tiles**:
- \(4x + 4\) can be represented as 4 x-tiles and 4 1-tiles.
- \(2x + 2\) can be represented as 2 x-tiles and 2 1-tiles.

2. **Setting Up the Expression**:
- Start with \(4x + 4\):
- **Tiles**: x x x x (4 x-tiles) and 1 1 1 1 (4 1-tiles).
- Subtract \(2x + 2\):
- **Tiles to remove**: x x (2 x-tiles) and 1 1 (2 1-tiles).

3. **Visualizing the Tiles**:
- **Start with**:
- \(4x\): x x x x
- \(+ 4\): 1 1 1 1
- **Subtract**:
- \(2x\): - x x
- \(+ 2\): - 1 - 1

4. **Combine Like Terms**:
- For the x-tiles:
- \(4x - 2x = 2x\)
- For the 1-tiles:
- \(4 - 2 = 2\)

5. **Final Expression**:
- After combining, we have:
- \(2x + 2\)

Thus, \((4x + 4) - (2x + 2) = 2x + 2\).

This means the simplified expression is: **\(2x + 2\)**.