Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
1,\\
3{x^2} - 4y + 4x - 3{y^2}\\
 = \left( {3{x^2} - 3{y^2}} \right) + \left( {4x - 4y} \right)\\
 = 3.\left( {{x^2} - {y^2}} \right) + 4.\left( {x - y} \right)\\
 = 3.\left( {x - y} \right)\left( {x + y} \right) + 4.\left( {x - y} \right)\\
 = \left( {x - y} \right).\left[ {3.\left( {x + y} \right) + 4} \right]\\
 = \left( {x - y} \right)\left( {3x + 3y + 4} \right)\\
2,\\
{\left( {4{x^2} - 7x - 50} \right)^2} - 16{x^4} - 56{x^3} - 49{x^2}\\
 = {\left( {4{x^2} - 7x - 50} \right)^2} - \left( {16{x^4} + 56{x^3} + 49{x^2}} \right)\\
 = {\left( {4{x^2} - 7x - 50} \right)^2} - \left[ {{{\left( {4{x^2}} \right)}^2} + 2.4{x^2}.7x + {{\left( {7x} \right)}^2}} \right]\\
 = {\left( {4{x^2} - 7x - 50} \right)^2} - {\left( {4{x^2} + 7x} \right)^2}\\
 = \left[ {\left( {4{x^2} - 7x - 50} \right) - \left( {4{x^2} + 7x} \right)} \right].\left[ {\left( {4{x^2} - 7x - 50} \right) + \left( {4{x^2} + 7x} \right)} \right]\\
 = \left( { - 14x - 50} \right).\left( {8{x^2} - 50} \right)\\
 = \left( { - 2} \right).\left( {7x + 25} \right).2.\left( {4{x^2} - 25} \right)\\
 =  - 4.\left( {7x + 25} \right)\left( {4{x^2} - 25} \right)\\
3,\\
{\left( {{x^2} + {y^2} - 5} \right)^2} - 4{x^2}.{y^2} - 16xy + 16\\
 = {\left( {{x^2} + {y^2} - 5} \right)^2} - \left( {4{x^2}{y^2} + 16xy + 16} \right)\\
 = {\left( {{x^2} + {y^2} - 5} \right)^2} - \left[ {{{\left( {2xy} \right)}^2} + 2.2xy.4 + {4^2}} \right]\\
 = {\left( {{x^2} + {y^2} - 5} \right)^2} - {\left( {2xy + 4} \right)^2}\\
 = \left[ {\left( {{x^2} + {y^2} - 5} \right) - \left( {2xy + 4} \right)} \right].\left[ {\left( {{x^2} + {y^2} - 5} \right) + \left( {2xy + 4} \right)} \right]\\
 = \left[ {\left( {{x^2} + {y^2} - 2xy} \right) - 9} \right].\left[ {\left( {{x^2} + 2xy + {y^2}} \right) - 1} \right]\\
 = \left[ {{{\left( {x - y} \right)}^2} - {3^2}} \right].\left[ {{{\left( {x + y} \right)}^2} - {1^2}} \right]\\
 = \left( {x - y - 3} \right)\left( {x - y + 3} \right).\left( {x + y - 1} \right)\left( {x + y + 1} \right)
\end{array}\)

\(\begin{array}{l}
4,\\
{x^6} + 3{x^4}{y^2} - 8{x^3}{y^3} + 3{x^2}{y^4} + {y^6}\\
 = \left( {{x^6} - 2{x^3}{y^3} + {y^6}} \right) + \left( {3{x^4}{y^2} - 6{x^3}{y^3} + 3{x^2}{y^4}} \right)\\
 = {\left( {{x^3} - {y^3}} \right)^2} + 3{x^2}{y^2}.\left( {{x^2} - 2xy + {y^2}} \right)\\
 = {\left( {{x^3} - {y^3}} \right)^2} + 3{x^2}{y^2}{\left( {x - y} \right)^2}\\
 = {\left[ {\left( {x - y} \right)\left( {{x^2} + xy + {y^2}} \right)} \right]^2} + 3{x^2}{y^2}{\left( {x - y} \right)^2}\\
 = {\left( {x - y} \right)^2}.\left[ {{{\left( {{x^2} + xy + {y^2}} \right)}^2} + 3{x^2}{y^2}} \right]
\end{array}\)