Đáp án:
\(\begin{array}{l}
a,\\
\left( {\sqrt x - 1} \right)\left( {\sqrt x - 2} \right)\\
b,\\
\left( {x - 2\sqrt y } \right)\left( {x - \sqrt y } \right)\\
c,\\
{\left( {\sqrt {x - 1} + 1} \right)^2}\\
d,\\
\sqrt x .\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right)\\
g,\\
\left( { - \sqrt x + 1} \right).\left( {6\sqrt x + 1} \right)\\
h,\\
\left( { - 3\sqrt x + 2} \right).\left( {2\sqrt x - 1} \right)\\
f,\\
\left( {\sqrt x + 1} \right)\left( {\sqrt x + 3} \right)\\
i,\\
\left( {2\sqrt a - 3\sqrt b } \right)\left( {\sqrt a + 2\sqrt b } \right)
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
x - 3\sqrt x + 2\\
= \left( {x - \sqrt x } \right) + \left( { - 2\sqrt x + 2} \right)\\
= \sqrt x .\left( {\sqrt x - 1} \right) - 2.\left( {\sqrt x - 1} \right)\\
= \left( {\sqrt x - 1} \right)\left( {\sqrt x - 2} \right)\\
b,\\
{x^2} - 3x\sqrt y + 2y\\
= \left( {{x^2} - 2x\sqrt y } \right) + \left( { - x\sqrt y + 2y} \right)\\
= x\left( {x - 2\sqrt y } \right) - \sqrt y .\left( {x - 2\sqrt y } \right)\\
= \left( {x - 2\sqrt y } \right)\left( {x - \sqrt y } \right)\\
c,\\
x + 2\sqrt {x - 1} \\
= \left( {x - 1} \right) + 2\sqrt {x - 1} + 1\\
= {\sqrt {x - 1} ^2} + 2.\sqrt {x - 1} .1 + {1^2}\\
= {\left( {\sqrt {x - 1} + 1} \right)^2}\\
d,\\
\sqrt {{x^3}} - 2\sqrt x - x\\
= x\sqrt x - 2\sqrt x - x\\
= \sqrt x .\left( {x - 2 - \sqrt x } \right)\\
= \sqrt x .\left[ {\left( {x - 2\sqrt x } \right) + \left( {\sqrt x - 2} \right)} \right]\\
= \sqrt x .\left[ {\sqrt x .\left( {\sqrt x - 2} \right) + \left( {\sqrt x - 2} \right)} \right]\\
= \sqrt x .\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right)\\
g,\\
- 6x + 5\sqrt x + 1\\
= \left( { - 6x + 6\sqrt x } \right) + \left( { - \sqrt x + 1} \right)\\
= 6\sqrt x .\left( { - \sqrt x + 1} \right) + \left( { - \sqrt x + 1} \right)\\
= \left( { - \sqrt x + 1} \right).\left( {6\sqrt x + 1} \right)\\
h,\\
7\sqrt x - 6x - 2\\
= \left( { - 6x + 4\sqrt x } \right) + \left( {3\sqrt x - 2} \right)\\
= 2\sqrt x .\left( { - 3\sqrt x + 2} \right) - \left( { - 3\sqrt x + 2} \right)\\
= \left( { - 3\sqrt x + 2} \right).\left( {2\sqrt x - 1} \right)\\
f,\\
x + 4\sqrt x + 3\\
= \left( {x + \sqrt x } \right) + \left( {3\sqrt x + 3} \right)\\
= \sqrt x .\left( {\sqrt x + 1} \right) + 3.\left( {\sqrt x + 1} \right)\\
= \left( {\sqrt x + 1} \right)\left( {\sqrt x + 3} \right)\\
i,\\
2a + \sqrt {ab} - 6b\\
= \left( {2a - 3\sqrt {ab} } \right) + \left( {4\sqrt {ab} - 6b} \right)\\
= \sqrt a .\left( {2\sqrt a - 3\sqrt b } \right) + 2\sqrt b \left( {2\sqrt a - 3\sqrt b } \right)\\
= \left( {2\sqrt a - 3\sqrt b } \right)\left( {\sqrt a + 2\sqrt b } \right)
\end{array}\)
