) Use algebra tiles to find \( \left(-8 x^{2}+8 x+6\right)-\left(-6 x^{2}+6 x\right) \)

To solve the expression \( \left(-8 x^{2}+8 x+6\right)-\left(-6 x^{2}+6 x\right) \) using algebra tiles, you can visualize or represent the polynomial using tiles where negative tiles are used to represent negative coefficients. 1. Start with the first polynomial: you would place 8 negative \(x^2\) tiles, 8 positive \(x\) tiles, and 6 positive unit tiles. 2. For the second polynomial, use 6 negative \(x^2\) tiles and 6 positive \(x\) tiles. 3. Subtracting the second polynomial means adding the opposite, so you will add 6 positive \(x^2\) tiles and 6 negative \(x\) tiles to your setup. 4. Combine the like terms: for \(x^2\) terms, you have \(-8 + 6 = -2\); for \(x\) terms, \(8 - 6 = 2\); and for the constant, you still have 6. Putting it all together, the result simplifies to \( -2x^2 + 2x + 6 \). With algebra tiles, visualizing negative and positive coefficients helps in grasping the concept of polynomials. Each set of tiles gives students a hands-on approach to better understand how to manipulate and simplify expressions!