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Câu 3:
a: \(=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
b: \(=\left(\sqrt{x}-\sqrt{y}\right)^2\)
c: \(=\sqrt{x}\left(\sqrt{y}+2\right)-3\left(\sqrt{y}+2\right)\)
\(=\left(\sqrt{y}+2\right)\left(\sqrt{x}-3\right)\)
c)
$\sqrt{a^3}-\sqrt{b^3}+\sqrt{a^2b}-\sqrt{ab^2}$
$=(\sqrt{a^3}+\sqrt{a^2b})-(\sqrt{b^3}+\sqrt{ab^2})$
$=\sqrt{a^2}(\sqrt{a}+\sqrt{b})-\sqrt{b^2}(\sqrt{b}+\sqrt{a})$
$=a(\sqrt{a}+\sqrt{b})-b(\sqrt{b}+\sqrt{a})$
$=(\sqrt{a}+\sqrt{b})(a-b)=(\sqrt{a}+\sqrt{b})^2(\sqrt{a}-\sqrt{b})$
d)
$x-y+\sqrt{xy^2}-\sqrt{y^3}$
$=(x-y)+(\sqrt{xy^2}-\sqrt{y^3})$
$=(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})+y(\sqrt{x}-\sqrt{y})$
$=(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y}+y)$
a)
$3-\sqrt{3}+\sqrt{15}-3\sqrt{15}$
$=\sqrt{3}(\sqrt{3}-1)-\sqrt{15}(3-1)$
$=(\sqrt{3}(\sqrt{3}-1)-\sqrt{15}(\sqrt{3}+1)(\sqrt{3}-1)$
$=(\sqrt{3}-1)[\sqrt{3}-\sqrt{15}(\sqrt{3}+1)]$
$=(\sqrt{3}-1)(\sqrt{3}-\sqrt{45}-\sqrt{15})$
b)
$\sqrt{1-a}+\sqrt{1-a^2}=\sqrt{1-a}+\sqrt{(1-a)(1+a)}$
$=\sqrt{1-a}+\sqrt{1-a}.\sqrt{1+a}=\sqrt{1-a}(1+\sqrt{1+a})$
a: \(=\dfrac{2\left(\sqrt{3}-2\right)}{2\left(\sqrt{2}-1\right)}-6\sqrt{2}\)
\(=\dfrac{-2+\sqrt{3}}{\sqrt{2}-1}-6\sqrt{2}\)
\(=\left(-2+\sqrt{3}\right)\left(\sqrt{2}+1\right)-6\sqrt{2}\)
\(=-2\sqrt{2}-2+\sqrt{6}+\sqrt{3}-6\sqrt{2}\)
\(=-8\sqrt{2}+\sqrt{6}+\sqrt{3}-2\)
b: \(=\dfrac{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}=\dfrac{\sqrt{a}}{\sqrt{b}}\)
c:\(=\dfrac{\left(1+\sqrt{x}\right)\left(1+\sqrt{y}\right)}{1+\sqrt{y}}=1+\sqrt{x}\)
d: \(=\dfrac{\left(x-\sqrt{3x}+3\right)}{\left(\sqrt{x}+\sqrt{3}\right)\left(x-\sqrt{3x}+3\right)}=\dfrac{1}{\sqrt{x}+\sqrt{3}}\)