\(A,ĐKXĐ:x;y\ge0\)

\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)

\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)

\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)

\(ĐKXĐ:x;y\ge0\)

\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)

\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)

\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)

\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)

\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)

\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)

a: \(\frac{\left(1+\sqrt{x}\right)^2-4\sqrt{x}}{1-\sqrt{x}}\)

\(=\frac{1+2\sqrt{x}+x-4\sqrt{x}}{1-\sqrt{x}}=\frac{1-2\sqrt{x}+x}{1-\sqrt{x}}\)

\(=\frac{\left(1-\sqrt{x}\right)^2}{1-\sqrt{x}}=1-\sqrt{x}=1-\sqrt2\)

b: \(\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+4\sqrt{xy}}{1+\sqrt{xy}}\)

\(=\frac{x-2\sqrt{xy}+y+4\sqrt{xy}}{1+\sqrt{xy}}=\frac{x+2\sqrt{xy}+y}{1+\sqrt{xy}}\)

\(=\frac{\left(\sqrt{x}+\sqrt{y}\right)^2}{1+\sqrt{xy}}=\frac{\left(\sqrt2+\sqrt3\right)^2}{1+\sqrt{2\cdot3}}=\frac{5+2\sqrt6}{1+\sqrt6}\)

\(=\frac{\left(5+2\sqrt6\right)\left(\sqrt6-1\right)}{5}=\frac{5\sqrt6-5+12-2\sqrt6}{5}=\frac{3\sqrt6+7}{5}\)

\(ab+b\sqrt{a}+\sqrt{a}+1\)

(đk: \(a\ge0\))

\(=b\sqrt{a}\left(\sqrt{a}+1\right)+\sqrt{a}+1=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)

ĐK: \(x,y\ge0\)

\(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}=x\left(\sqrt{x}+\sqrt{y}\right)-y\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(x-y\right)\)

\(=\left(\sqrt{x}+\sqrt{y}\right)^2\left(\sqrt{x}-\sqrt{y}\right)\)

1/ Thực hiện phép tính

a) √9−2√20+√12−2√35

 \(=\sqrt{\left(\sqrt{5}-\sqrt{4}\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}\)

\(=\sqrt{5}-\sqrt{4}+\sqrt{7}-\sqrt{5}=\sqrt{7}-\sqrt{4}=\sqrt{7}-2\)

a) 2a−4b=2(a−2b)2a−4b=2(a−2b)

c) 2ax−2ay+2a=2a(x−y+1)2ax−2ay+2a=2a(x−y+1)

e) 3xy(x−4)−9x(4−x)=3x(x−4)(y+3)3xy(x−4)−9x(4−x)=3x(x−4)(y+3)

b,d xem lại đề

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