Rút gọn các biểu thức sau: \( \frac{1}{2}{x^2}\left( {6x - 3} \right) - x\left( {{x^2} + \frac{1}{2}} \right) + \frac{1}{2}\left( {x + 4} \right)\)

* Hướng dẫn giải

Ta có:

\(\begin{array}{l} \frac{1}{2}{x^2}\left( {6x - 3} \right) - x\left( {{x^2} + \frac{1}{2}} \right) + \frac{1}{2}\left( {x + 4} \right)\\ = \frac{1}{2}{x^2}.6x - \frac{1}{2}{x^2}.3 - x.{x^2} - x.\frac{1}{2} + \frac{1}{2}x + \frac{1}{2}.4\\ = 3{x^3} - \frac{3}{2}{x^2} - {x^3} - \frac{1}{2}x + \frac{1}{2}x + 2 = (3{x^3} - {x^3}) - \frac{3}{2}{x^2} - \frac{1}{2}x + \frac{1}{2}x + 2\\ = 2{x^3} - \frac{3}{2}{x^2} + 2 \end{array}\)