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

Question

UpStudy AI · Accepted Answer

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

### Understanding Algebra Tiles

**Algebra tiles** are a visual tool that represent different types of terms:
- **Positive $$x^2$$ tiles** and **negative $$x^2$$ tiles** represent quadratic terms.
- **Positive $$x$$ tiles** and **negative $$x$$ tiles** represent linear terms.
- **Positive and negative unit tiles** represent constant terms.

For this problem, we'll focus on $$x^2$$ and $$x$$ tiles.

### Step 1: Represent Each Expression with Algebra Tiles

1. **First Expression: $$-9x^{2} + 9x$$**
   - **$$-9x^{2}$$**: 9 **negative $$x^2$$ tiles**
   - **$$+9x$$**: 9 **positive $$x$$ tiles**

2. **Second Expression: $$-9x^{2} + x$$**
   - **$$-9x^{2}$$**: 9 **negative $$x^2$$ tiles**
   - **$$+x$$**: 1 **positive $$x$$ tile**

### Step 2: Subtract the Second Expression from the First

When subtracting the second expression, it's equivalent to adding the opposite of each term in the second expression:

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

This is because:
- Subtracting $$-9x^{2}$$ is the same as adding $$9x^{2}$$.
- Subtracting $$x$$ is the same as adding $$-x$$.

### Step 3: Combine Like Terms Using Algebra Tiles

Now, let's combine the terms:

1. **Quadratic Terms ($$x^2$$)**:
   - $$-9x^{2} + 9x^{2} = 0x^{2}$$
   - The $$x^2$$ tiles cancel each other out.

2. **Linear Terms ($$x$$)**:
   - $$9x - x = 8x$$
   - Combining the $$x$$ tiles results in $$8x$$.

### Final Result

After simplifying, the expression reduces to:

$$
\left(-9x^{2} + 9x\right) - \left(-9x^{2} + x\right) = 8x
$$

### Visual Summary with Algebra Tiles

- **Quadratic Tiles**: $$-9x^{2}$$ and $$+9x^{2}$$ cancel each other out.
- **Linear Tiles**: $$+9x$$ minus $$x$$ leaves $$+8x$$.

Therefore, the final simplified expression is:

$$
\boxed{8x}
$$
The simplified expression is $$8x$$.

Use algebra tiles to find

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions