Đáp án:
$\begin{array}{l}
d)2xy - {x^2} + 3{y^2} - 4y + 1\\
= 4{y^2} - 4y + 1 - {x^2} + 2xy - {y^2}\\
= {\left( {2y - 1} \right)^2} - {\left( {x - y} \right)^2}\\
= \left( {2y - 1 - x + y} \right)\left( {2y - 1 + x - y} \right)\\
= \left( {3y - x - 1} \right)\left( {y + x - 1} \right)\\
e)8{x^2} - 12xy + 4{y^2} - 2x - 1\\
= 9{x^2} - 12xy + 4{y^2} - {x^2} - 2x - 1\\
= {\left( {3x - 2y} \right)^2} - {\left( {x + 1} \right)^2}\\
= \left( {3x - 2y + x + 1} \right)\left( {3x - 2y - x - 1} \right)\\
= \left( {4x - 2y + 1} \right)\left( {2x - 2y - 1} \right)\\
f)625{t^9} + 75{t^3} + 9\\
= {\left( {25{t^3}} \right)^2} + 2.25{t^3}.3 + 9 - 75{t^3}\\
= {\left( {25{t^3} + 3} \right)^2} - 75{t^3}\\
= \left( {25{t^3} + 3 - \sqrt {75{t^3}} } \right)\left( {25{t^3} + 3 + \sqrt {75{t^3}} } \right)\\
g)4{x^{16}} + 81\\
= 4{x^{16}} + 2.2{x^8}.9 + 81 - 2.2{x^8}.9\\
= {\left( {2{x^8} + 9} \right)^2} - 36{x^8}\\
= \left( {2{x^8} + 6{x^4} + 9} \right)\left( {2{x^8} - 6{x^4} + 9} \right)
\end{array}$
