\[\begin{array}{l}
A){X^2} - 4{X^2}{y^2} + {y^2} + 2xy\\
= {x^2} + 2xy + {y^2} - 4{x^2}{y^2}\\
= {\left( {x + y} \right)^2} - {\left( {2xy} \right)^2}\\
= \left( {x + y - 2xy} \right)\left( {x + y + 2xy} \right)\\
B){(4{x^2} - 25)^2} - 9{(2x - 5)^2}\\
= {\left( {4{x^2} - 25} \right)^2} - {\left( {6x - 15} \right)^2}\\
= \left( {4{x^2} - 25 - 6x + 15} \right)\left( {4{x^2} - 25 + 6x - 15} \right)\\
= \left( {4{x^2} - 6x - 10} \right)\left( {4{x^2} + 6x - 40} \right)\\
= 4\left( {2{x^2} - 3x - 5} \right)\left( {2{x^2} + 3x - 20} \right)\\
= 4\left( {x + 1} \right)\left( {2x - 5} \right)\left( {2x - 5} \right)\left( {x + 4} \right)\\
= 4\left( {x + 1} \right){\left( {2x - 5} \right)^2}\left( {x + 4} \right)\\
c)4{(2x - 3)^2} - 9{(4{x^2} - 9)^2}\\
= {\left( {4x - 6} \right)^2} - {\left( {12{x^2} - 27} \right)^2}\\
= \left( {4x - 6 - 12{x^2} + 27} \right)\left( {4x - 6 + 12{x^2} - 27} \right)\\
= \left( { - 12{x^2} + 4x + 21} \right)\left( {12{x^2} + 4x - 33} \right)\\
= \left( {2x - 3} \right)\left( {6x + 7} \right)\left( {2x - 3} \right)\left( {6x + 11} \right)\\
= {\left( {2x - 3} \right)^2}\left( {6x + 7} \right)\left( {6x + 11} \right)\\
D){a^6} - {a^4} + 2{a^3} + 2{a^2}\\
= {a^2}\left( {{a^4} - {a^2} + 2a + 2} \right)\\
= {a^2}\left[ {{a^2}\left( {{a^2} - 1} \right) + 2\left( {a + 1} \right)} \right]\\
= {a^2}\left[ {{a^2}\left( {a - 1} \right)\left( {a + 1} \right) + 2\left( {a + 1} \right)} \right]\\
= {a^2}\left( {a + 1} \right)\left( {{a^3} - {a^2} + 2} \right)\\
= {a^2}\left( {a + 1} \right)\left( {a + 1} \right)\left( {{a^2} - 2a + 2} \right)\\
E){(3{x^2} + 3x + 2)^2} - {(3{x^2} + 3x - 2)^2}\\
= \left( {3{x^2} + 3x + 2 - 3{x^2} - 3x + 2} \right)\left( {3{x^2} + 3x + 2 + 3{x^2} + 3x - 2} \right)\\
= 4\left( {6{x^2} + 6x} \right)\\
= 24x\left( {x + 1} \right)
\end{array}\]