algebra tiles to find \( \left(8 x^{2}-10 x+4\right)-\left(4 x^{2}+1\right) \)

To subtract the polynomials \( (8x^{2} - 10x + 4) - (4x^{2} + 1) \) using algebra tiles, follow these steps: ### **1. Understanding Algebra Tiles:** Algebra tiles are visual tools that represent different parts of a polynomial: - **\(x^{2}\) tiles:** Typically larger squares. - **\(x\) tiles:** Rectangles. - **Constant tiles:** Small squares. For subtraction, you'll remove the tiles representing the second polynomial from the first. ### **2. Represent Each Polynomial with Algebra Tiles:** **First Polynomial: \(8x^{2} - 10x + 4\)** - **\(8x^{2}\) tiles:** 8 large square tiles. - **\(-10x\) tiles:** 10 negative rectangle tiles (often represented with a different color or marked with a negative sign). - **\(+4\) tiles:** 4 small square tiles. **Second Polynomial: \(4x^{2} + 1\)** - **\(4x^{2}\) tiles:** 4 large square tiles. - **\(+1\) tile:** 1 small square tile. ### **3. Subtract the Second Polynomial:** To subtract \( (4x^{2} + 1) \), remove the corresponding tiles from the first polynomial: - **Remove \(4x^{2}\) tiles:** Subtract 4 large square tiles from the 8. - **Remove \(+1\) tile:** Subtract 1 small square tile from the 4. ### **4. Calculate the Remaining Tiles:** - **\(x^{2}\) tiles:** \(8x^{2} - 4x^{2} = 4x^{2}\) - **\(x\) tiles:** No \(x\) tiles to remove from the second polynomial, so it remains \(-10x\). - **Constant tiles:** \(4 - 1 = 3\) ### **5. Combine the Results:** After subtraction, the resulting polynomial is: \[ 4x^{2} - 10x + 3 \] ### **Final Answer:** \[ (8x^{2} - 10x + 4) - (4x^{2} + 1) = 4x^{2} - 10x + 3 \]