1) Use algebra tiles to find \( \left(-3 x^{2}+8\right)+\left(-7 x^{2}-10 x-8\right) \)

To find the sum of the two polynomials \((-3x^{2} + 8)\) and \((-7x^{2} - 10x - 8)\) using algebra tiles, follow these steps: ### Step 1: Represent Each Polynomial with Algebra Tiles 1. **First Polynomial \((-3x^{2} + 8)\):** - **\(-3x^{2}\):** Use 3 negatively marked \(x^{2}\) tiles. - **\(+8\):** Use 8 positively marked unit tiles. 2. **Second Polynomial \((-7x^{2} - 10x - 8)\):** - **\(-7x^{2}\):** Use 7 negatively marked \(x^{2}\) tiles. - **\(-10x\):** Use 10 negatively marked \(x\) tiles. - **\(-8\):** Use 8 negatively marked unit tiles. ### Step 2: Combine Like Terms by Adding the Tiles 1. **Combine \(x^{2}\) Tiles:** - \(-3x^{2}\) (from the first polynomial) and \(-7x^{2}\) (from the second polynomial) add up to \(-10x^{2}\). 2. **Combine \(x\) Tiles:** - Only \(-10x\) exists in the second polynomial. 3. **Combine Unit Tiles:** - \(+8\) (from the first polynomial) and \(-8\) (from the second polynomial) cancel each other out, resulting in \(0\). ### Step 3: Write the Final Simplified Expression After combining all like terms, the simplified expression is: \[ -10x^{2} - 10x \] ### Conclusion Using algebra tiles to visualize and combine like terms, the sum of \((-3x^{2} + 8)\) and \((-7x^{2} - 10x - 8)\) is: \[ -10x^{2} - 10x \]