Đáp án:

\(\begin{array}{l}
a,\\
2{x^2}y.\left( {x - y + 3} \right)\left( {x + y - 3} \right)\\
b,\\
\left( {2x + 5} \right).\left( {3x - 1} \right)\\
c,\\
\left( {2{x^2} - 6x + 9} \right).\left( {2{x^2} + 6x + 9} \right)
\end{array}\)

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
a,\\
2{x^4}y - 2{x^2}{y^3} + 12{x^2}{y^2} - 18{x^2}y\\
 = 2{x^2}y.{x^2} - 2{x^2}y.{y^2} + 2{x^2}y.6y - 2{x^2}y.9\\
 = 2{x^2}y\left( {{x^2} - {y^2} + 6y - 9} \right)\\
 = 2{x^2}y.\left[ {{x^2} - \left( {{y^2} - 6y + 9} \right)} \right]\\
 = 2{x^2}y.\left[ {{x^2} - \left( {{y^2} - 2.y.3 + {3^2}} \right)} \right]\\
 = 2{x^2}y.\left[ {{x^2} - {{\left( {y - 3} \right)}^2}} \right]\\
 = 2{x^2}y.\left[ {x - \left( {y - 3} \right)} \right].\left[ {x + \left( {y - 3} \right)} \right]\\
 = 2{x^2}y.\left( {x - y + 3} \right)\left( {x + y - 3} \right)\\
b,\\
6{x^2} + 13x - 5\\
 = \left( {6{x^2} + 15x} \right) + \left( { - 2x - 5} \right)\\
 = 3x.\left( {2x + 5} \right) - \left( {2x + 5} \right)\\
 = \left( {2x + 5} \right).\left( {3x - 1} \right)\\
c,\\
4{x^4} + 81\\
 = \left( {4{x^4} + 36{x^2} + 81} \right) - 36{x^2}\\
 = \left[ {{{\left( {2{x^2}} \right)}^2} + 2.2{x^2}.9 + {9^2}} \right] - 36{x^2}\\
 = {\left( {2{x^2} + 9} \right)^2} - {\left( {6x} \right)^2}\\
 = \left[ {\left( {2{x^2} + 9} \right) - 6x} \right].\left[ {\left( {2{x^2} + 9} \right) + 6x} \right]\\
 = \left( {2{x^2} - 6x + 9} \right).\left( {2{x^2} + 6x + 9} \right)
\end{array}\)