Question

Use algebra tiles to find (8x2+3)–(4x2+1).
x2
x2
x2
x2
x2
x2
x2
x2
1
1
1
–
x2
x2
x2
x2
1
Combine like terms. For example, write 3 instead of 1 + 1 + 1.

Answer 1

To solve the expression \( (8x^2 + 3) - (4x^2 + 1) \) using algebra tiles, we follow these steps:

1. **Set up the expression**:
- You have \( 8x^2 \) tiles and \( 3 \) unit tiles.
- You also have \( 4x^2 \) tiles and \( 1 \) unit tile that will be subtracted from the first expression.

2. **Visualize the tiles**:
- \( 8x^2 \) tiles can be represented as:
\[
x^2, x^2, x^2, x^2, x^2, x^2, x^2, x^2
\]
- \( 3 \) unit tiles can be represented as:
\[
1, 1, 1
\]
- For \( 4x^2 \) tiles, we have:
\[
x^2, x^2, x^2, x^2
\]
- And \( 1 \) unit tile:
\[
1
\]

3. **Subtract the tiles**:
- **Subtract** \( 4x^2 \) from \( 8x^2 \):
- Start with \( 8x^2 \) tiles:
\[
x^2, x^2, x^2, x^2, x^2, x^2, x^2, x^2
\]
- Remove \( 4x^2 \) tiles:
\[
x^2, x^2, x^2, x^2
\]
- Remaining tiles are:
\[
x^2, x^2, x^2, x^2
\]
(This gives us \( 4x^2 \))

- **Subtract** \( 1 \) from \( 3 \):
- Start with \( 3 \) unit tiles:
\[
1, 1, 1
\]
- Remove \( 1 \) unit tile:
\[
1
\]
- Remaining tiles are:
\[
1, 1
\]
(This gives us \( 2 \))

4. **Combine like terms**:
- After the subtraction, we have \( 4x^2 + 2 \).

Thus, the result of the expression \( (8x^2 + 3) - (4x^2 + 1) \) is:
\[
\boxed{4x^2 + 2}
\]