Đáp án:
\(\begin{array}{l}
3)\dfrac{1}{8}{x^6} + \dfrac{1}{4}{x^4}y + \dfrac{1}{6}{x^2}{y^2} + \dfrac{1}{{27}}{y^3}\\
4)27{x^6} - 54{x^4}{y} + 36{x^2}{y^2} - 8{y^3}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{*{20}{l}}
{3){{\left( {\dfrac{1}{2}{x^2} + \dfrac{1}{3}y} \right)}^3}}\\
{ = {{\left( {\dfrac{1}{2}{x^2}} \right)}^3} + 3.{{\left( {\dfrac{1}{2}{x^2}} \right)}^2}.\dfrac{1}{3}y + 3.\dfrac{1}{2}{x^2}.{{\left( {\dfrac{1}{3}y} \right)}^2} + {{\left( {\dfrac{1}{3}y} \right)}^3}}\\
{ = \dfrac{1}{8}{x^6} + \dfrac{1}{4}{x^4}y + \dfrac{1}{6}{x^2}{y^2} + \dfrac{1}{{27}}{y^3}}\\
{4){{\left( {3{x^2} - 2y} \right)}^3}}\\
{ = {{\left( {3{x^2}} \right)}^3} - 3.{{\left( {3{x^2}} \right)}^2}.2y + 3.3{x^2}.{{\left( {2y} \right)}^2} - {{\left( {2y} \right)}^3}}\\
{ = 27{x^6} - 54{x^4}y + 36{x^2}{y^2} - 8{y^3}}
\end{array}\)
