Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
a,\\
\left( {5{x^2} + 9xy - 2{y^2}} \right):\left( {x + 2y} \right)\\
 = \left[ {\left( {5{x^2} + 10xy} \right) - \left( {xy + 2{y^2}} \right)} \right]:\left( {x + 2y} \right)\\
 = \left[ {5x\left( {x + 2y} \right) - y\left( {x + 2y} \right)} \right]:\left( {x + 2y} \right)\\
 = \left[ {\left( {x + 2y} \right)\left( {5x - y} \right)} \right]:\left( {x + 2y} \right)\\
 = 5x - y\\
b,\\
\left( {{x^4} - {x^3}y + {x^2}{y^2} - x{y^3}} \right):\left( {{x^2} + {y^2}} \right)\\
 = \left[ {\left( {{x^4} - {x^3}y} \right) + \left( {{x^2}{y^2} - x{y^3}} \right)} \right]:\left( {{x^2} + {y^2}} \right)\\
 = \left[ {{x^3}\left( {x - y} \right) + x{y^2}\left( {x - y} \right)} \right]:\left( {{x^2} + {y^2}} \right)\\
 = \left[ {\left( {x - y} \right).\left( {{x^3} + x{y^2}} \right)} \right]:\left( {{x^2} + {y^2}} \right)\\
 = \left[ {\left( {x - y} \right).x\left( {{x^2} + {y^2}} \right)} \right]:\left( {{x^2} + {y^2}} \right)\\
 = x\left( {x - y} \right)\\
d,\\
\left( {2{a^3} + 7a{b^2} - 7{a^2}b - 2{b^3}} \right):\left( {2a - b} \right)\\
 = \left[ {\left( {2{a^3} - {a^2}b} \right) - \left( {6{a^2}b - 3a{b^2}} \right) + \left( {4a{b^2} - 2{b^3}} \right)} \right]:\left( {2a - b} \right)\\
 = \left[ {{a^2}\left( {2a - b} \right) - 3ab\left( {2a - b} \right) + 2{b^2}\left( {2a - b} \right)} \right]:\left( {2a - b} \right)\\
 = \left[ {\left( {2a - b} \right)\left( {{a^2} - 3ab + 2{b^2}} \right)} \right]:\left( {2a - b} \right)\\
 = {a^2} - 3ab + 2{b^2}
\end{array}\)