Đáp án:

\(\begin{array}{l}
b,\\
\left( {x - 2y} \right)\left( {x - 2y - 2} \right)\\
f,\\
\left( {{x^2} + 2x + 2} \right).\left( {{x^2} - 2x + 2} \right)\\
g,\\
\left( {{x^4} - {x^2} + 1} \right)\left( {{x^4} + {x^2} + 1} \right)\\
h,\\
\left( {x - y} \right).\left( {{x^2} + 11xy + 8{y^2}} \right)\\
i,\\
\left( {x - y + 2z} \right).\left( {{x^2} + {y^2} + 4{z^2} + xy - 2xz + 2yz} \right)\\
k,\\
\left( {x - y} \right)\left( {y - z} \right).\left( {x - z} \right).\left( {x + y + z} \right)
\end{array}\)

Giải thích các bước giải:

\(\begin{array}{l}
b,\\
{x^2} + 4{y^2} - 4xy - 2x + 4y\\
 = \left( {{x^2} - 4xy + 4{y^2}} \right) + \left( { - 2x + 4y} \right)\\
 = \left[ {{x^2} - 2.x.2y + {{\left( {2y} \right)}^2}} \right] - 2.\left( {x - 2y} \right)\\
 = {\left( {x - 2y} \right)^2} - 2\left( {x - 2y} \right)\\
 = \left( {x - 2y} \right).\left[ {\left( {x - 2y} \right) - 2} \right]\\
 = \left( {x - 2y} \right)\left( {x - 2y - 2} \right)\\
f,\\
{x^4} + 4\\
 = \left( {{x^4} + 4{x^2} + 4} \right) - 4{x^2}\\
 = \left[ {{{\left( {{x^2}} \right)}^2} + 2.{x^2}.2 + {2^2}} \right] - {\left( {2x} \right)^2}\\
 = {\left( {{x^2} + 2} \right)^2} - {\left( {2x} \right)^2}\\
 = \left[ {\left( {{x^2} + 2} \right) + 2x} \right].\left[ {\left( {{x^2} + 2} \right) - 2x} \right]\\
 = \left( {{x^2} + 2x + 2} \right).\left( {{x^2} - 2x + 2} \right)\\
g,\\
{x^8} + {x^4} + 1\\
 = \left( {{x^8} + 2{x^4} + 1} \right) - {x^4}\\
 = \left[ {{{\left( {{x^4}} \right)}^2} + 2.{x^4}.1 + {1^2}} \right] - {\left( {{x^2}} \right)^2}\\
 = {\left( {{x^4} + 1} \right)^2} - {\left( {{x^2}} \right)^2}\\
 = \left[ {\left( {{x^4} + 1} \right) - {x^2}} \right].\left[ {\left( {{x^4} + 1} \right) + {x^2}} \right]\\
 = \left( {{x^4} - {x^2} + 1} \right)\left( {{x^4} + {x^2} + 1} \right)\\
h,\\
{x^3} + 10{x^2}y - 3x{y^2} - 8{y^3}\\
 = \left( {{x^3} - {x^2}y} \right) + \left( {11{x^2}y - 11x{y^2}} \right) + \left( {8x{y^2} - 8{y^3}} \right)\\
 = {x^2}\left( {x - y} \right) + 11xy\left( {x - y} \right) + 8{y^2}\left( {x - y} \right)\\
 = \left( {x - y} \right).\left( {{x^2} + 11xy + 8{y^2}} \right)\\
i,\\
{x^3} - {y^3} + 8{z^3} + 6xyz\\
 = \left( {{x^3} - 3{x^2}y + 3x{y^2} - {y^3}} \right) + 8{z^3} + 3{x^2}y - 3x{y^2} + 6xyz\\
 = {\left( {x - y} \right)^3} + {\left( {2z} \right)^3} + 3xy.\left( {x - y + 2z} \right)\\
 = \left[ {\left( {x - y} \right) + 2z} \right].\left[ {{{\left( {x - y} \right)}^2} - \left( {x - y} \right).2z + {{\left( {2z} \right)}^2}} \right] + 3xy\left( {x - y + 2z} \right)\\
 = \left( {x - y + 2z} \right).\left( {{x^2} - 2xy + {y^2} - 2xz + 2yz + 4{z^2}} \right) + 3xy\left( {x - y + 2z} \right)\\
 = \left( {x - y + 2z} \right).\left[ {\left( {{x^2} - 2xy + {y^2} - 2xz + 2yz + 4{z^2}} \right) + 3xy} \right]\\
 = \left( {x - y + 2z} \right).\left( {{x^2} + {y^2} + 4{z^2} + xy - 2xz + 2yz} \right)\\
k,\\
{x^3}.\left( {y - z} \right) + {y^3}\left( {z - x} \right) + {z^3}\left( {x - y} \right)\\
 = {x^3}\left( {y - z} \right) + {y^3}z - {y^3}x + {z^3}x - {z^3}y\\
 = {x^3}\left( {y - z} \right) + \left( {{y^3}z - {z^3}y} \right) + \left( { - {y^3}x + {z^3}x} \right)\\
 = {x^3}\left( {y - z} \right) + yz\left( {{y^2} - {z^2}} \right) - x.\left( {{y^3} - {z^3}} \right)\\
 = {x^3}\left( {y - z} \right) + yz\left( {y - z} \right)\left( {y + z} \right) - x.\left( {y - z} \right).\left( {{y^2} + yz + {z^2}} \right)\\
 = {x^3}\left( {y - z} \right) + \left( {{y^2}z + y{z^2}} \right)\left( {y - z} \right) - \left( {y - z} \right).\left( {x{y^2} + xyz + x{z^2}} \right)\\
 = \left( {y - z} \right).\left[ {{x^3} + \left( {{y^2}z + y{z^2}} \right) - \left( {x{y^2} + xyz + x{z^2}} \right)} \right]\\
 = \left( {y - z} \right).\left[ {\left( {{x^3} - x{y^2}} \right) + \left( {{y^2}z - xyz} \right) + \left( {y{z^2} - x{z^2}} \right)} \right]\\
 = \left( {y - z} \right).\left[ {x\left( {{x^2} - {y^2}} \right) + yz.\left( {y - x} \right) + {z^2}\left( {y - x} \right)} \right]\\
 = \left( {y - z} \right).\left[ {x\left( {x - y} \right)\left( {x + y} \right) - yz\left( {x - y} \right) - {z^2}\left( {x - y} \right)} \right]\\
 = \left( {y - z} \right).\left( {x - y} \right).\left[ {x\left( {x + y} \right) - yz - {z^2}} \right]\\
 = \left( {y - z} \right)\left( {x - y} \right)\left( {{x^2} + xy - yz - {z^2}} \right)\\
 = \left( {y - z} \right)\left( {x - y} \right).\left[ {\left( {{x^2} - {z^2}} \right) + \left( {xy - yz} \right)} \right]\\
 = \left( {x - y} \right)\left( {y - z} \right).\left[ {\left( {x - z} \right)\left( {x + z} \right) + y.\left( {x - z} \right)} \right]\\
 = \left( {x - y} \right)\left( {y - z} \right).\left( {x - z} \right).\left( {x + y + z} \right)
\end{array}\)