Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
{\left( {{x^2} - \frac{1}{{2x}}} \right)^4} = \sum\limits_{k = 0}^4 {C_4^k.{{\left( {{x^2}} \right)}^{4 - k}}.{{\left( { - \frac{1}{{2x}}} \right)}^k} = \sum\limits_{k = 0}^4 {C_4^k.{x^{8 - 2k}}.{{\left( { - \frac{1}{2}} \right)}^k}.} {x^{ - k}}} \\
= \sum\limits_{k = 0}^4 {C_4^k.{{\left( { - \frac{1}{2}} \right)}^k}.{x^{8 - 3k}}} \\
= C_4^0.{x^8} + C_4^1.\frac{{ - 1}}{2}.{x^5} + C_4^2.\frac{1}{4}.{x^2} + C_4^3.\frac{{ - 1}}{8}.{x^{ - 1}} + C_4^4.\frac{1}{{16}}.{x^{ - 4}}\\
= {x^8} - 2{x^5} + \frac{3}{2}{x^2} - \frac{1}{{2x}} + \frac{1}{{16{x^4}}}
\end{array}\]
