Đáp án:
\(\begin{array}{l}
2,\\
a,\,\,\,\,\left( {x - y} \right)\left( {x - 2} \right)\\
b,\,\,\,\,{\left( {x - 1} \right)^2}.{\left( {x + 1} \right)^2}\\
3,\,\,\,\,9{y^3}\\
4,\\
a,\,\,\,4016000\\
b,\,\,\,\,1000000\\
c,\,\,\,\,200\\
5,\\
a,\\
\left[ \begin{array}{l}
x = 0\\
x = 4\\
x = - 4
\end{array} \right.\\
b,\\
\left[ \begin{array}{l}
x = 3\\
x = 1
\end{array} \right.
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
2,\\
a,\\
{x^2} - 2x + 2y - xy\\
= \left( {{x^2} - xy} \right) + \left( { - 2x + 2y} \right)\\
= x.\left( {x - y} \right) - \left( {2x - 2y} \right)\\
= x\left( {x - y} \right) - 2.\left( {x - y} \right)\\
= \left( {x - y} \right)\left( {x - 2} \right)\\
b,\\
{\left( {{x^2} + 1} \right)^2} - 4{x^2}\\
= {\left( {{x^2} + 1} \right)^2} - {\left( {2x} \right)^2}\\
= \left[ {\left( {{x^2} + 1} \right) - 2x} \right].\left[ {\left( {{x^2} + 1} \right) + 2x} \right]\\
= \left( {{x^2} - 2x + 1} \right)\left( {{x^2} + 2x + 1} \right)\\
= \left( {{x^2} - 2.x.1 + {1^2}} \right).\left( {{x^2} + 2.x.1 + {1^2}} \right)\\
= {\left( {x - 1} \right)^2}.{\left( {x + 1} \right)^2}\\
3,\\
\left( {x + 2y} \right).\left( {{x^2} - 2xy + 4{y^2}} \right) - \left( {x - y} \right).\left( {{x^2} + xy + {y^2}} \right)\\
= \left( {x + 2y} \right).\left( {{x^2} - x.2y + {{\left( {2y} \right)}^2}} \right) - \left( {x - y} \right)\left( {{x^2} + x.y + {y^2}} \right)\\
= \left[ {{x^3} + {{\left( {2y} \right)}^3}} \right] - \left( {{x^3} - {y^3}} \right)\\
= \left( {{x^3} + 8{y^3}} \right) - \left( {{x^3} - {y^3}} \right)\\
= {x^3} + 8{y^3} - {x^3} + {y^3}\\
= 9{y^3}\\
4,\\
a,\\
{2004^2} - 16 = {2004^2} - {4^2}\\
= \left( {2004 - 4} \right).\left( {2004 + 4} \right)\\
= 2000.2008\\
= 4016000\\
b,\\
{892^2} + 892.216 + {108^2}\\
= {892^2} + 892.2.108 + {108^2}\\
= {892^2} + 2.892.108 + {108^2}\\
= {\left( {892 + 108} \right)^2}\\
= {1000^2}\\
= 1000000\\
c,\\
10,2.9,8 - 9,8.0,2 + {10,2^2} - 10,2.0,2\\
= \left( {10,2.9,8 + {{10,2}^2}} \right) - \left( {9,8.0,2 + 10,2.0,2} \right)\\
= 10,2.\left( {9,8 + 10,2} \right) - 0,2.\left( {9,8 + 10,2} \right)\\
= 10,2.20 - 0,2.20\\
= 20.\left( {10,2 - 0,2} \right)\\
= 20.10\\
= 200\\
5,\\
a,\\
{x^3} - 16x = 0\\
\Leftrightarrow x.\left( {{x^2} - 16} \right) = 0\\
\Leftrightarrow x.\left( {{x^2} - {4^2}} \right) = 0\\
\Leftrightarrow x.\left( {x - 4} \right).\left( {x + 4} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x - 4 = 0\\
x + 4 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 4\\
x = - 4
\end{array} \right.\\
b,\\
{x^2} - 4x + 3 = 0\\
\Leftrightarrow {x^2} - 4x + 4 = 1\\
\Leftrightarrow {x^2} - 2.x.2 + {2^2} = 1\\
\Leftrightarrow {\left( {x - 2} \right)^2} = 1\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2 = 1\\
x - 2 = - 1
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = 1
\end{array} \right.
\end{array}\)
