Use algebra tiles to find $$ \left(7 x^{2}-3 x+6\right)+(10 x-7) $$

Question

UpStudy AI · Accepted Answer

Certainly! Let's use the concept of **algebra tiles** to add the two polynomials $$ (7x^{2} - 3x + 6) $$ and $$ (10x - 7) $$.

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

1. **First Polynomial: $$ 7x^{2} - 3x + 6 $$**
   - **7** $$ x^{2} $$ tiles
   - **-3** $$ x $$ tiles
   - **+6** unit tiles

2. **Second Polynomial: $$ 10x - 7 $$**
   - **10** $$ x $$ tiles
   - **-7** unit tiles

### Step 2: Combine Like Terms

When adding polynomials, **like terms** (terms with the same variable and exponent) are combined by adding their coefficients.

1. **$$ x^{2} $$ Terms:**
   - Only from the first polynomial: **7** $$ x^{2} $$ tiles
   - **Total:** $$ 7x^{2} $$

2. **$$ x $$ Terms:**
   - From the first polynomial: **-3** $$ x $$ tiles
   - From the second polynomial: **+10** $$ x $$ tiles
   - **Combined:** $$ -3x + 10x = 7x $$

3. **Constant (Unit) Terms:**
   - From the first polynomial: **+6** units
   - From the second polynomial: **-7** units
   - **Combined:** $$ 6 - 7 = -1 $$

### Step 3: Write the Resulting Polynomial

After combining like terms, the sum of the two polynomials is:

$$
7x^{2} + 7x - 1
$$

### Visual Summary with Algebra Tiles

- **$$ x^{2} $$ Tiles:** 7 (no combining needed)
- **$$ x $$ Tiles:** $$ -3 + 10 = 7 $$
- **Unit Tiles:** $$ 6 - 7 = -1 $$

So, the final combined polynomial is:

$$
7x^{2} + 7x - 1
$$
The sum of the polynomials is $$ 7x^{2} + 7x - 1 $$.

Use algebra tiles to find

Upstudy AI Solution

Answer

Solution

Step 1: Represent Each Polynomial with Algebra Tiles

Step 2: Combine Like Terms

Step 3: Write the Resulting Polynomial

Visual Summary with Algebra Tiles

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