2. Simplify: (6x^3-x^2-5x+4)-(4x^3-6x^2-3x+4)

To simplify the expression \((6x^{3}-x^{2}-5x+4)-(4x^{3}-6x^{2}-3x+4)\), we need to distribute the negative sign to each term in the second polynomial and then combine like terms.<br /><br />First, distribute the negative sign:<br /><br />\[<br />(6x^{3} - x^{2} - 5x + 4) - (4x^{3} - 6x^{2} - 3x + 4) = 6x^{3} - x^{2} - 5x + 4 - 4x^{3} + 6x^{2} + 3x - 4<br />\]<br /><br />Next, combine like terms:<br /><br />\[<br />(6x^{3} - 4x^{3}) + (-x^{2} + 6x^{2}) + (-5x + 3x) + (4 - 4)<br />\]<br /><br />Simplify each group of like terms:<br /><br />\[<br />2x^{3} + 5x^{2} - 2x + 0<br />\]<br /><br />So, the simplified expression is:<br /><br />\[<br />2x^{3} + 5x^{2} - 2x<br />\]