d)) Use algebra tiles to find $$ \left(-9 x^{2}+9 x\right)-\left(-9 x^{2}+x\right) $$

Question

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To solve $$ \left(-9x^{2} + 9x\right) - \left(-9x^{2} + x\right) $$ using **algebra tiles**, let's break down the problem step-by-step.

### Understanding Algebra Tiles

Algebra tiles are visual representations used to model algebraic expressions. Each term in the expression is represented by a specific tile:

- **Positive $$x^{2}$$ tile**: Typically a large square.
- **Negative $$x^{2}$$ tile**: A large square of a different color (e.g., red).
- **Positive $$x$$ tile**: A rectangle.
- **Negative $$x$$ tile**: A rectangle of a different color (e.g., red).
- **Positive constant tile**: A small square.
- **Negative constant tile**: A small square of a different color (e.g., red).

### Step-by-Step Solution

1. **Represent Each Expression with Tiles:**

- **First Expression:** $$ -9x^{2} + 9x $$
     - **-9 $$x^{2}$$ Tiles:** 9 large red squares.
     - **+9 $$x$$ Tiles:** 9 rectangles.

- **Second Expression:** $$ -9x^{2} + x $$
     - **-9 $$x^{2}$$ Tiles:** 9 large red squares.
     - **+1 $$x$$ Tile:** 1 rectangle.

2. **Set Up the Subtraction:**

$$
   \left(-9x^{2} + 9x\right) - \left(-9x^{2} + x\right)
   $$

Subtracting the second expression is equivalent to adding its additive inverse:

$$
   \left(-9x^{2} + 9x\right) + \left(+9x^{2} - x\right)
   $$

3. **Combine Like Terms:**

- **$$x^{2}$$ Terms:**
     - $$ -9x^{2} + 9x^{2} = 0x^{2} $$
     - The large red squares cancel each other out.

- **$$x$$ Terms:**
     - $$ +9x - x = +8x $$
     - You are left with 8 positive $$x$$ rectangles.

4. **Final Representation:**

After cancellation, the only tiles remaining are **8 positive $$x$$** rectangles.

### Conclusion

Using algebra tiles, subtracting $$ \left(-9x^{2} + x\right) $$ from $$ \left(-9x^{2} + 9x\right) $$ results in:

$$
8x
$$

**Answer:** $$8x$$
The result is $$8x$$.

d)) Use algebra tiles to find

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