Show using algebra tiles that 3x and x - 1 are the factors of 3x ^ 2 - 3x Draw the tiles here.

To visualize the factoring of \( 3x^2 - 3x \) using algebra tiles, we can represent the expression using area models, where each tile corresponds to a different part of the algebraic expression.

### Tiles Representations:

1. **\( x^2 \) Tile**: This is a large square representing \( x^2 \).
2. **\( x \) Tile**: This is a rectangle representing \( x \).
3. **Unit Tile**: This is a small square representing the constant 1 (but will not be used here).

### Given Expression: \( 3x^2 - 3x \)

- **\( 3x^2 \)**: This is represented by 3 large square tiles.
- **\( -3x \)**: This is represented by 3 rectangle tiles, each corresponding to \( -x \).

### Factorization Process:

- **Factor 1: \( 3x \)**: This corresponds to 3 rows of \( x \) tiles.
- **Factor 2: \( x - 1 \)**: This corresponds to 1 row of \( x \) tile and 1 row of \(-1\) tiles.

### Drawing the Tiles:

Let's visualize the tiles based on the above explanation.

\[
\begin{array}{c|c|c}
\textbf{x} & \textbf{x} & \textbf{x} \\ \hline
x^2 & x^2 & x^2 \\ \hline
-x & -x & -x \\
\end{array}
\]

In the grid:

- **First row**: Represents \( 3x^2 \) using three \( x^2 \) tiles.
- **Second row**: Represents \( -3x \) using three \( -x \) tiles.

### Factorization Interpretation:

- The rows correspond to the factors \( 3x \) and \( x - 1 \).
- The overall area (product of these factors) corresponds to the original expression \( 3x^2 - 3x \).

This shows that \( 3x^2 - 3x \) can be factored into \( 3x(x - 1) \) using algebra tiles.

Do you want details or have any questions? 

Here are 8 related questions:
1. How can algebra tiles be used to factor a quadratic expression with a constant term?
2. What is the purpose of using algebra tiles in understanding algebraic expressions?
3. How would the algebra tiles change if the expression had a positive constant term?
4. Can algebra tiles be used to visualize the expansion of binomials? How?
5. How do algebra tiles represent negative terms in an expression?
6. What other algebraic methods can be used to factor \( 3x^2 - 3x \)?
7. How can you use algebra tiles to verify the distributive property?
8. How would you factor a trinomial using algebra tiles?

**Tip:** Algebra tiles are a visual way to understand and teach algebraic concepts, making abstract ideas more concrete.

Learn how to use algebra tiles to visually demonstrate that 3x and x - 1 are factors of the quadratic expression 3x^2 - 3x. This detailed explanation includes step-by-step visualization using algebraic tiles, suitable for students in Grades 7-9 studying algebra and quadratic equations.

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