Giải thích các bước giải:
\[\begin{array}{l}
1,\\
\left( {2x - 1} \right)\left( {2x + 1} \right) + \left( {4{x^3} - 2x} \right):x\\
= {\left( {2x} \right)^2} - {1^2} + \left[ {x\left( {4{x^2} - 2} \right)} \right]:x\\
= 4{x^2} - 1 + 4{x^2} - 2\\
= 8{x^2} - 3\\
2,\\
a,\\
{x^2} - 2xy - 9 + {y^2} = \left( {{x^2} - 2xy + {y^2}} \right) - 9\\
= {\left( {x - y} \right)^2} - {3^2} = \left( {x - y - 3} \right)\left( {x - y + 3} \right)\\
b,\\
{x^3} - 8 + 2x\left( {x - 2} \right) = \left( {{x^3} - {2^3}} \right) + 2x\left( {x - 2} \right)\\
= \left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right) + 2x\left( {x - 2} \right)\\
= \left( {x - 2} \right)\left( {{x^2} + 4x + 4} \right)\\
= \left( {x - 2} \right){\left( {x + 2} \right)^2}
\end{array}\]
