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\(Sửa:x+y-9-2\sqrt{xy}\\ =\left(\sqrt{x}-\sqrt{y}\right)^2-9=\left(\sqrt{x}-\sqrt{y}-3\right)\left(\sqrt{x}-\sqrt{y}+3\right)\)
a: =(căn a-3)^2-b^2
=(căn a-3-b)(căn a-3+b)
b: \(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)
c: \(x-7\sqrt{x}+12=x-3\sqrt{x}-4\sqrt{x}+12=\left(\sqrt{x}-3\right)\left(\sqrt{x}-4\right)\)
d: x*căn x-64
=(căn x)^3-4^3
=(căn x-4)(x+4căn x+16)
\(a-6\sqrt{a}+9-b^2\\ =\left(\sqrt{a}+3\right)^2-b^2\\ =\left(\sqrt{a}+3-b\right)\left(\sqrt{a}+3+b\right)\)
\(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)
\(x-7\sqrt{x}+12\\ =x-4\sqrt{x}-3\sqrt{x}+12\\ =\sqrt{x}\left(\sqrt{x}-4\right)-3\left(\sqrt{x}-4\right)\\ =\left(\sqrt{x}-4\right)\left(\sqrt{x}-3\right)\)
\(x\sqrt{x}+64\\ =\sqrt{x^3}+4^3\\ =\left(\sqrt{x}\right)^3+4^3\\ =\left(\sqrt{x}+4\right)\left(x-4\sqrt{x}+16\right)\)
\(=\left(x^2-6x+9\right)-4y^2\)
\(=\left(x-3\right)^2-\left(2y\right)^2\)
\(=\left(x-3-2y\right)\left(x-3+2y\right)\)
= ( x^2 - 4y^2 ) + ( 9 - 6x)
= [ x^2 - (2y)^2 ] + 3( 3 - 2x )
= (x - 2y)(x + 2y)+ 3(3 - 2x)
1) \(x\sqrt{y}+y\sqrt{x}=\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\)
2) \(9-6\sqrt{a}+a=\left(\sqrt{a}-3\right)^2\)
3) \(a+2\sqrt{ab}+b=\left(\sqrt{a}+\sqrt{b}\right)^2\)
4) \(x-y+\sqrt{x}+\sqrt{y}=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}+1\right)\)
5) \(a+2\sqrt{ab}+b-1=\left(\sqrt{a}+\sqrt{b}\right)^2-1=\left(\sqrt{a}+\sqrt{b}-1\right)\left(\sqrt{a}+\sqrt{b}+1\right)\)
1) \(x\sqrt{y}+y\sqrt{x}=\sqrt{x}\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)\)
2) \(9-6\sqrt{a}+a=\left(3-\sqrt{a}\right)^2\)
3) \(a+2\sqrt{ab}+b=\left(\sqrt{a}+\sqrt{b}\right)^2\)
4) \(x-y+\sqrt{x}+\sqrt{y}=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}+1\right)\)
5) \(a+2\sqrt{ab}+b-1=\left(\sqrt{a}+\sqrt{b}\right)^2-1^2=\left(\sqrt{a}+\sqrt{b}-1\right)\left(\sqrt{a}+\sqrt{b}+1\right)\)
\(x-\sqrt{x}-6=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\)
\(2x+5\sqrt{x}-3=\left(\sqrt{x}+3\right)\left(2\sqrt{x}-1\right)\)
<=>x9-9x6-27
<=>(x3)3-3(x3)23+3.9.x3-27-27x3
<=>(x3-3)3-27x3
<=>(x3-3-3x).((x3-3)2+(x3-3).3x+9x2)
<=>(x3-3-3x).(x6-6x3+9+3x4-9x+9x2)
\(\left(x-3\right).\left(x+3\right)\)\(+\left(x-3\right)\left(x+4\right)\)=\(\left(x-3\right)\left(x+3+x+4\right)=\left(x-3\right)\left(2x+7\right)\)
`4a+1(a<=0=>-a>=0)`
`=1-4(-a)`
`=1-(2sqrt{-a})^2`
`=(1-2sqrt{-a})(1+2sqrt{-a})`