Đáp án+Giải thích các bước giải:
$\begin{array}{l}
4{x^2} - 2{y^2} + 1999{\left( {2x - y} \right)^2}\\
= 4{x^2} - 2{y^2} + 1999\left( {4{x^2} - 4xy + {y^2}} \right)\\
= 8000{x^2} - 7996xy + 1997{y^2}\\
= {\left( {40x\sqrt 5 } \right)^2} - 2.40x\sqrt 5 .\dfrac{{1999y}}{{20\sqrt 5 }} + {\left( {\dfrac{{1999y}}{{20\sqrt 5 }}} \right)^2} - \dfrac{{2001{y^2}}}{{2000}}\\
= {\left( {40x\sqrt 5 - \dfrac{{1999y}}{{20\sqrt 5 }}} \right)^2} - {\left( {\dfrac{{y\sqrt {2001} }}{{20\sqrt 5 }}} \right)^2}\\
= \left( {40x\sqrt 5 - \dfrac{{1999y}}{{20\sqrt 5 }} - \dfrac{{y\sqrt {2001} }}{{20\sqrt 5 }}} \right)\left( {40x\sqrt 5 - \dfrac{{1999y}}{{20\sqrt 5 }} + \dfrac{{y\sqrt {2001} }}{{20\sqrt 5 }}} \right)\\
= \left( {40\sqrt 5 - \dfrac{{y\left( {1999 + \sqrt {2001} } \right)}}{{20\sqrt 5 }}} \right)\left( {40\sqrt 5 - \dfrac{{y\left( {1999 - \sqrt {2001} } \right)}}{{20\sqrt 5 }}} \right)
\end{array}$
