)) Use algebra tiles to find $$ \left(x^{2}+5 x\right)+\left(8 x^{2}+8 x+3\right) $$

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UpStudy AI · Accepted Answer

Certainly! Let's use **algebra tiles** to add the two polynomials:

$$
\left(x^{2} + 5x\right) + \left(8x^{2} + 8x + 3\right)
$$

**Algebra Tiles Overview:**
- **$$ x^2 $$ tile**: Represents the quadratic term.
- **$$ x $$ tile**: Represents the linear term.
- **$$ 1 $$ tile**: Represents the constant term.

**Step 1: Represent Each Polynomial with Algebra Tiles**

1. **First Polynomial: $$ x^{2} + 5x $$**
   - **$$ x^2 $$ tiles**: 1
   - **$$ x $$ tiles**: 5
   - **$$ 1 $$ tiles**: 0

![First Polynomial Tiles](https://i.imgur.com/1P9Yb1K.png)

2. **Second Polynomial: $$ 8x^{2} + 8x + 3 $$**
   - **$$ x^2 $$ tiles**: 8
   - **$$ x $$ tiles**: 8
   - **$$ 1 $$ tiles**: 3

![Second Polynomial Tiles](https://i.imgur.com/YkMFWZD.png)

**Step 2: Combine the Tiles**

Add the corresponding tiles from both polynomials:

- **Total $$ x^2 $$ tiles**: $$1 + 8 = 9$$
- **Total $$ x $$ tiles**: $$5 + 8 = 13$$
- **Total $$ 1 $$ tiles**: $$0 + 3 = 3$$

![Combined Tiles](https://i.imgur.com/4yQqV9s.png)

**Step 3: Write the Resulting Polynomial**

Combine the totals to form the final polynomial:

$$
9x^{2} + 13x + 3
$$

**Final Answer:**
$$
(x^{2} + 5x) + (8x^{2} + 8x + 3) = 9x^{2} + 13x + 3
$$

**Visualization Summary:**

1. **First Polynomial:**
   - $$ x^2 $$ tile × 1
   - $$ x $$ tile × 5

2. **Second Polynomial:**
   - $$ x^2 $$ tile × 8
   - $$ x $$ tile × 8
   - $$ 1 $$ tile × 3

3. **Combined:**
   - $$ x^2 $$ tile × 9
   - $$ x $$ tile × 13
   - $$ 1 $$ tile × 3

By organizing and combining the algebra tiles, we systematically add like terms to arrive at the simplified polynomial.
Combine like terms to get $$ 9x^{2} + 13x + 3 $$.

)) Use algebra tiles to find

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