Giải thích các bước giải:
$\begin{array}{l}
a)10{x^3}y - 5{x^2}{y^2} - 25{x^4}{y^3} = - 5xy\left( { - 2{x^2} + xy + 5{x^3}{y^2}} \right)\\
\Rightarrow \left( {10{x^3}y - 5{x^2}{y^2} - 25{x^4}{y^3}} \right):\left( { - 5xy} \right) = - 2{x^2} + xy + 5{x^3}{y^2}\\
b)15{(x - y)^5} - 9{(x - y)^4} + 12{(y - x)^2} = {\left( {x - y} \right)^2}\left( {15{{\left( {x - y} \right)}^3} - 9{{\left( {x - y} \right)}^2} + 12} \right)\\
\Rightarrow \left( {15{{(x - y)}^5} - 9{{(x - y)}^4} + 12{{(y - x)}^2}} \right):{\left( {x - y} \right)^2} = 15{\left( {x - y} \right)^3} - 9{\left( {x - y} \right)^2} + 12\\
\Rightarrow \left( {15{{(x - y)}^5} - 9{{(x - y)}^4} + 12{{(y - x)}^2}} \right):{\left( {y - x} \right)^2} = 15{\left( {x - y} \right)^3} - 9{\left( {x - y} \right)^2} + 12\\
c)27{x^3} - {y^3} = {\left( {3x} \right)^3} - {y^3} = \left( {3x - y} \right)\left( {9{x^2} + 3xy + {y^2}} \right)\\
\Rightarrow \left( {27{x^3} - {y^3}} \right):\left( {3x - y} \right) = 9{x^2} + 3xy + {y^2}\\
d)15{x^4} + 4{x^3} + 11{x^2} + 14x - 8\\
= 3{x^2}\left( {5{x^2} + 3x - 2} \right) - x\left( {5{x^2} + 3x - 2} \right) + 4\left( {5{x^2} + 3x - 2} \right)\\
= \left( {5{x^2} + 3x - 2} \right)\left( {3{x^2} - x + 4} \right)\\
\Rightarrow \left( {15{x^4} + 4{x^3} + 11{x^2} + 14x - 8} \right):\left( {5{x^2} + 3x - 2} \right) = 3{x^2} - x + 4
\end{array}$
