Question

Use algebra tiles to find (3x2+6x+6)+(8x+9).
x2
x2
x2
x
x
x
x
x
x
1
1
1
1
1
1
+
x
x
x
x
x
x
x
x
1
1
1
1
1
1
1
1
1
Combine like terms. For example, write 3 instead of 1 + 1 + 1.

Answer 1

To solve the expression \( (3x^2 + 6x + 6) + (8x + 9) \) using algebra tiles and then combine like terms, we proceed as follows:

1. **Identify and represent the terms using algebra tiles**:
- **For \(3x^2\)**: Use 3 algebra tiles for \(x^2\).
- **For \(6x\)**: Use 6 algebra tiles for \(x\).
- **For \(6\)**: Use 6 unit tiles (1).
- **For \(8x\)**: Use 8 additional algebra tiles for \(x\).
- **For \(9\)**: Use 9 additional unit tiles (1).

2. **Count all the terms**:
- Total \(x^2\) terms: 3 (from the first part)
- Total \(x\) terms: \(6 + 8 = 14\)
- Total constant terms: \(6 + 9 = 15\)

3. **Combine like terms**:
- **For \(x^2\)**: There are 3 \(x^2\) tiles, so this remains \(3x^2\).
- **For \(x\)**: Combine the \(14\) \(x\) tiles, so this becomes \(14x\).
- **For the constants**: Combine the \(15\) unit tiles, so this becomes \(15\).

Putting all together, we find:
\[
3x^2 + 14x + 15
\]

Thus, the simplified result of \( (3x^2 + 6x + 6) + (8x + 9) \) is:
\[
\boxed{3x^2 + 14x + 15}
\]