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a: \(A=x\sqrt{x}-y\sqrt{y}+x\sqrt{y}-y\sqrt{x}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)
b: \(B=5x^2-7x\sqrt{y}+2y\)
\(=5x^2-5x\sqrt{y}-2x\sqrt{y}+2y\)
\(=5x\left(x-\sqrt{y}\right)-2\sqrt{y}\left(x-\sqrt{y}\right)\)
\(=\left(x-\sqrt{y}\right)\left(5x-2\sqrt{y}\right)\)
\(A,ĐKXĐ:x;y\ge0\)
\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)
\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)
\(ĐKXĐ:x;y\ge0\)
\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)
\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)
a: \(\frac12x^2-2y^2=\frac12\left(x^2-4y^2\right)\)
\(=\frac12\left(x-2y\right)\left(x+2y\right)\)
b: \(\frac13xy+x^2z+xz\)
\(=x\cdot\frac13y+x\cdot xz+x\cdot z\)
\(=x\left(\frac13y+xz+z\right)\)
c: \(18x^3-\frac{8}{25}x=2x\left(9x^2-\frac{4}{25}\right)\)
\(=2x\left\lbrack\left(3x\right)^2-\left(\frac25\right)^2\right\rbrack\)
\(=2x\left(3x-\frac25\right)\left(3x+\frac25\right)\)
d: \(\frac25x^2+5x^3+x^2y=x^2\cdot\frac25+x^2\cdot5x+x^2\cdot y=x^2\left(\frac25+5x+y\right)\)
e: \(\frac12\left(x^2+y^2\right)^2-2x^2y^2\)
\(=\frac12\left\lbrack\left(x^2+y^2\right)^2-4x^2y^2\right\rbrack\)
\(=\frac12\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)\)
\(=\frac12\left(x-y\right)^2\cdot\left(x+y\right)^2\)
f: \(27x^3-\frac18y^3=\left(3x\right)^3-\left(\frac12y\right)^3\)
\(=\left(3x-\frac12y\right)\left(9x^2+\frac32xy+\frac14y^2\right)\)
với a,b,x,y không âm ta có
a,\(ab+b\sqrt{a}+\sqrt{a}+1\)
\(=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
b, \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)
a. \(ab+b\sqrt{a}+\sqrt{a}+1=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
b. \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(x+2\sqrt{xy}+y\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)