)) Use algebra tiles to find \( \left(4 x^{2}+4 x-3\right)-\left(3 x^{2}+x+1\right) \)

To solve \( \left(4 x^{2}+4 x-3\right)-\left(3 x^{2}+x+1\right) \) using algebra tiles, you can visualize each term with corresponding tiles. Start with 4 "x²" tiles, 4 "x" tiles, and 3 negative unit tiles (to represent -3). Then, for the expression you are subtracting, you’ll use 3 "x²" tiles, 1 "x" tile, and 1 positive unit tile (to represent +1). Now, to perform the operation, take away the tiles from the second expression. After removing the 3 "x²" tiles, you will have 1 "x²" tile remaining. Then, take away the 1 "x" tile, leaving you with 3 "x" tiles. Finally, when you remove 1 positive unit tile from your negative unit tiles, you end up with 4 negative unit tiles total. So, putting it all together, you will have: \[ x^{2} + 3x - 4 \] The final simplified expression is: \[ x^{2} + 3x - 4 \] This fun tile method visually demonstrates how algebra can work in a tactile way! Now, if we turn this into an application you might find useful, consider how algebra tiles can help in teaching students who are struggling with polynomial expressions. By using these visual tools, learners can grasp the concept of combining like terms in a more interactive way. Also, when solving expressions like this one, a common mistake is forgetting to distribute the negative sign correctly when subtracting. It may lead to errors in your final answer, so always double-check that the sign of each term has been applied correctly!