第42页 - 启东中学作业本八年级数学苏科版宿迁专版

因式分解

D

$4\sqrt{3}$

$10\sqrt 5$

$ \begin{aligned}解:原式&=\sqrt 6×\sqrt 6×\sqrt 10 \\ &=6\sqrt{10} \\ \end{aligned}$

$解:原式=6×\sqrt {75}$

$\hspace{1.4cm}=6×\sqrt {25}×\sqrt 3$

$\hspace{1.4cm}=30\sqrt{3}$

$ \begin{aligned}解:原式&=12×3×\frac {\sqrt 2}{4} \\ &=9\sqrt{2} \\ \end{aligned}$

$ \begin{aligned}解:原式&=12×\sqrt {27} \\ &=12×\sqrt 9×\sqrt 3 \\ &=36\sqrt{3} \\ \end{aligned}$

$ \begin{aligned}解:原式&=4×\sqrt {xy×\frac 1y} \\ &=4\sqrt x \\ \end{aligned}$

$ \begin{aligned} 解:原式&=6×\sqrt {50ab} \\ &=6×\sqrt {25}×\sqrt {2ab} \\ &=30\sqrt{2ab} \\ \end{aligned}$

$解:∵0＜x＜y，$

$∴x-y＜0，$

$∴原式=(x+2y)(y-x).$

$ \begin{aligned} 解:原式&=\sqrt {125×25×y^5z^5} \\ &=\sqrt {25×25×y^4z^4}×\sqrt {5yz} \\ &=25y^2z^2 \sqrt{5yz} \\ \end{aligned}$

$ \begin{aligned}解:原式&=\sqrt {a(a^4+2a^2b^2+b^4)} \\ &=\sqrt {a(a^2+b^2)^2} \\ &=(a^2+b^2) \sqrt{a} \\ \end{aligned}$

$ \begin{aligned}解:原式&=\sqrt {16a^2(a+2)} \\ &=4a\sqrt{a+2} \\ \end{aligned}$