)) Use algebra tiles to find \( \left(10 x^{2}+7 x\right)+\left(x^{2}+10 x+5\right) \)

To find the sum of the polynomials \( \left(10x^{2} + 7x\right) + \left(x^{2} + 10x + 5\right) \) using **algebra tiles**, follow these steps: ### **1. Understand Algebra Tiles** Algebra tiles are visual tools that represent different types of terms in a polynomial: - **Square tiles** represent squared terms (\(x^2\)). - **Rectangular tiles** represent linear terms (\(x\)). - **Small square tiles** represent constant terms (numbers). ### **2. Represent Each Polynomial with Tiles** **First Polynomial: \(10x^{2} + 7x\)** - **10 square tiles** for \(10x^{2}\). - **7 rectangular tiles** for \(7x\). - **0 constant tiles** since there is no constant term. **Second Polynomial: \(x^{2} + 10x + 5\)** - **1 square tile** for \(x^{2}\). - **10 rectangular tiles** for \(10x\). - **5 constant tiles** for \(5\). ### **3. Combine the Tiles** Place all the tiles together: - **Square Tiles:** - \(10x^{2}\) + \(1x^{2}\) = **11 square tiles**. - **Rectangular Tiles:** - \(7x\) + \(10x\) = **17 rectangular tiles**. - **Constant Tiles:** - \(0\) + \(5\) = **5 constant tiles**. ### **4. Write the Combined Polynomial** After combining like terms, the resulting polynomial is: \[ 11x^{2} + 17x + 5 \] ### **Summary** Using algebra tiles, by grouping and combining like tiles (squares for \(x^2\), rectangles for \(x\), and units for constants), the sum of \( \left(10x^{2} + 7x\right) + \left(x^{2} + 10x + 5\right) \) simplifies to: \[ \boxed{11x^{2} + 17x + 5} \]