)) Use algebra tiles to find \( \left(7 x^{2}+5 x-6\right)-(-10 x-3) \)

To solve the expression \( \left(7x^{2} + 5x - 6\right) - \left(-10x - 3\right) \) using algebra tiles, let's break it down step by step. ### Step 1: Understand the Components 1. **First Polynomial:** \( 7x^{2} + 5x - 6 \) - **\(7x^{2}\)**: Represents seven \(x^2\) tiles. - **\(5x\)**: Represents five \(x\) tiles. - **\(-6\)**: Represents six negative unit tiles. 2. **Second Polynomial (to be subtracted):** \( -10x - 3 \) - **\(-10x\)**: Represents ten negative \(x\) tiles. - **\(-3\)**: Represents three negative unit tiles. ### Step 2: Subtract the Second Polynomial Subtracting \( (-10x - 3) \) is equivalent to adding its opposite: \[ \left(7x^{2} + 5x - 6\right) + \left(10x + 3\right) \] ### Step 3: Combine Like Terms Using Algebra Tiles 1. **Combine \(x^2\) Terms:** - \(7x^{2}\) remains as there are no other \(x^2\) terms to combine. 2. **Combine \(x\) Terms:** - \(5x + 10x = 15x\) 3. **Combine Constant Terms:** - \(-6 + 3 = -3\) ### Step 4: Write the Final Expression Combine all the simplified terms: \[ 7x^{2} + 15x - 3 \] ### Visual Representation with Algebra Tiles While I can't provide a visual diagram here, here's how you can imagine the tiles: - **Positive Tiles:** - 7 \(x^2\) tiles - 15 \(x\) tiles - **Negative Tiles:** - 3 negative unit tiles Arrange the tiles accordingly to represent the final simplified expression. ### Final Answer \[ 7x^{2} + 15x - 3 \]