Đáp án:
$\begin{array}{l}
1)\\
a)\left( {2x - y} \right)\left( {4{x^2} - 2xy + {y^2}} \right)\\
= \left( {2x - y} \right)\left( {{{\left( {2x} \right)}^2} - 2xy + {y^2}} \right)\\
= {\left( {2x} \right)^3} - {y^3}\\
= 8{x^3} - {y^3}\\
b)\left( {6{x^5}{y^2} - 9{x^4}{y^3} + 15{x^3}{y^4}} \right):3{x^3}{y^2}\\
= 3{x^3}{y^2}\left( {2{x^2} - 3xy + 5{y^2}} \right):3{x^3}{y^2}\\
= 2{x^2} - 3xy + 5{y^2}\\
c)\left( {2{x^3} - 21{x^2} + 67x - 60} \right):\left( {x - 5} \right)\\
= \left( {2{x^3} - 10{x^2} - 11{x^2} + 55x + 12x - 60} \right):\left( {x - 5} \right)\\
= \left( {x - 5} \right)\left( {2{x^2} - 11x + 12} \right):\left( {x - 5} \right)\\
= 2{x^2} - 11x + 12\\
2)\\
a){\left( {x + y} \right)^2} - {\left( {x - y} \right)^2}\\
= \left( {x + y + x - y} \right)\left( {x + y - x + y} \right)\\
= 2x.2y\\
= 4xy\\
4)\\
a){x^2} - {y^2} - 2x + 2y\\
= \left( {x - y} \right)\left( {x + y} \right) - 2\left( {x - y} \right)\\
= \left( {x - y} \right)\left( {x + y - 2} \right)\\
b)2x + 2y - {x^2} - xy\\
= 2\left( {x + y} \right) - x\left( {x + y} \right)\\
= \left( {x + y} \right)\left( {2 - x} \right)\\
c)3{a^2} - 6ab + 3{b^2} - 12{c^2}\\
= 3\left( {{a^2} - 2ab + {b^2} - 4{c^2}} \right)\\
= 3\left[ {{{\left( {a - b} \right)}^2} - {{\left( {2c} \right)}^2}} \right]\\
= 3\left( {a - b - 2c} \right)\left( {a - b + 2c} \right)
\end{array}$
