Question

Use algebra tiles to find (9x2+10x+5)–(x+2).
x2
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Combine like terms. For example, write 3 instead of 1 + 1 + 1.

Answer 1

To solve the expression \((9x^2 + 10x + 5) - (x + 2)\) using algebra tiles, we can visualize the process with the tiles representing each term.

1. **Visualize the Term Elements**:
- We have \(9x^2\) tiles (for \(9x^2\)), \(10x\) tiles (for \(10x\)), and \(5\) unit tiles (for \(5\)).
- We subtract \(x\) tile (for \(-x\)) and \(2\) unit tiles (for \(-2\)) from the total.

2. **Set Up the Tiles**:
- **Before Subtraction**:
- \(9\) tiles representing \(x^2\).
- \(10\) tiles representing \(x\).
- \(5\) tiles representing \(1\).

- **Subtract the Second Expression**:
- We take away \(1\) tile representing \(x\).
- We take away \(2\) unit tiles representing \(1\).

3. **Count the Tiles**:
- After subtracting \(1x\), the total number of \(x\) tiles will be: \(10 - 1 = 9\).
- After subtracting \(2\), the total number of unit tiles will be: \(5 - 2 = 3\).

4. **Combine Like Terms**:
- Now we have:
- \(9x^2\) tiles (stays the same),
- \(9x\) tiles (after subtraction),
- \(3\) unit tiles (after subtraction).

5. **Final Expression**:
- Combining these, we arrive at \(9x^2 + 9x + 3\).

Thus, the result of \((9x^2 + 10x + 5) - (x + 2)\) is:

\[
\boxed{9x^2 + 9x + 3}
\]