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

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: \[ 7x^{2} + 7x - 1 \]