(7x^4-9x^3-4x^2+5x+6)-(2x^4+3x^3-x^2+x-4) square square

To solve the given expression, we need to subtract the second polynomial from the first polynomial. Let's break it down step by step:<br /><br />Given expression:<br />\[<br />(7x^{4} - 9x^{3} - 4x^{2} + 5x + 6) - (2x^{4} + 3x^{3} - x^{2} + x - 4)<br />\]<br /><br />First, distribute the negative sign through the second polynomial:<br />\[<br />7x^{4} - 9x^{3} - 4x^{2} + 5x + 6 - 2x^{4} - 3x^{3} + x^{2} - x + 4<br />\]<br /><br />Next, combine like terms:<br />\[<br />(7x^{4} - 2x^{4}) + (-9x^{3} - 3x^{3}) + (-4x^{2} + x^{2}) + (5x - x) + (6 + 4)<br />\]<br /><br />Simplify each group of like terms:<br />\[<br />5x^{4} - 12x^{3} - 3x^{2} + 4x + 10<br />\]<br /><br />So, the simplified form of the given expression is:<br />\[<br />\boxed{5x^{4} - 12x^{3} - 3x^{2} + 4x + 10}<br />\]