)) Use algebra tiles to find \( \left(10 x^{2}-8 x+9\right)-\left(6 x^{2}-7 x\right) \)

To solve the expression \( \left(10 x^{2}-8 x+9\right)-\left(6 x^{2}-7 x\right) \) using algebra tiles, start by representing each term with tiles: - Use 10 large squares for \(10x^2\), 8 small tiles reversed for \(-8x\), and 9 unit tiles for \(+9\). - For the second expression, use 6 large squares for \(6x^2\) and 7 small tiles reversed for \(-7x\). Now, combine the tiles by removing the tiles from the second expression. You'll have \(10 - 6 = 4\) large squares (\(4x^2\)), \(-8 + 7 = -1\) small tile, and 9 unit tiles left. Thus, the final simplified expression is \(4x^2 - x + 9\). Let's summarize the neat result: \(4x^2 - x + 9\). Algebra tiles make this visual and fun, turning abstract numbers into a tangible puzzle to piece together! Next, think about how this could be applied. In real life, algebra tiles and similar visual tools can make understanding polynomials easier in classrooms, allowing students to physically manipulate terms—much like playing a board game! Whether in division or factoring polynomials, these manipulatives help grasp intricate concepts while playing!