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\(=\left(x^2-6x+9\right)-2=\left(x-3\right)^2-\sqrt{2^2}=\left(x-3-\sqrt{2}\right)\left(x-3+\sqrt{2}\right)\)
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\(=\left(x^2-6x+9\right)-4y^2\)
\(=\left(x-3\right)^2-\left(2y\right)^2\)
\(=\left(x-3-2y\right)\left(x-3+2y\right)\)
= ( x^2 - 4y^2 ) + ( 9 - 6x)
= [ x^2 - (2y)^2 ] + 3( 3 - 2x )
= (x - 2y)(x + 2y)+ 3(3 - 2x)
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x^2 - 10x - 16
= x^2 - 2.x.5 + 25 - 25 - 1 6
= ( x - 5)^2 - 41
=( x - 5 )^2 - \(\left(\sqrt{41}\right)^2\)
= ( x - 5 - căn 41 ) ( x - 5 + căn 41)
thang Tran làm thế hơi rảnh
của mjk
x2-10x-16
=x2-2x-8x-16
=x(x-2)-8(x-2)
=(x-2)(x-8)
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\(x^2-16+2\left(x+4\right)\)
\(=\left(x+4\right)\left(x-4\right)+2\left(x+4\right)\)
\(=\left(x+4\right)\left(x-4+2\right)\)
\(=\left(x+4\right)\left(x-2\right)\)
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Ta có: \(x^2+y^2+2xy+x+y-6\)
\(=\left(x+y\right)^2+x+y-6\)
\(=\left(x+y\right)^2+x+y-9+3\)
\(=\left[\left(x+y\right)^2-3^2\right]+\left(x+y+3\right)\)
\(=\left(x+y-3\right)\left(x+y+3\right)+\left(x+y+3\right)\)
\(=\left(x+y+3\right)\left(x+y-2\right)\)
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\(x^4-2y^4-x^2y^2+x^2+y^2=\left(x^4-y^4\right)-\left(x^2y^2-x^2\right)+\left(y^2-y^4\right)=\left(x^2-y^2\right)\left(x^2+y^2\right)-x^2\left(y^2-1\right)-y^2\left(y^2-1\right)=\left(x^2+y^2\right)\left(x^2-y^2\right)-\left(y^2-1\right)\left(x^2+y^2\right)=\left(x^2+y^2\right)\left(x^2-y^2-y^2+1\right)=\left(x^2+y^2\right)\left(x^2-2y^2+1\right)\)
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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) \(a+2\sqrt{ab}+b-1=\left(\sqrt{a}+\sqrt{b}\right)^2-1^2=\left(\sqrt{a}+\sqrt{b}-1\right)\left(\sqrt{a}+\sqrt{b}+1\right)\)
\(=x^2-\left(y-4\right)^2\)
\(=\left(x-y+4\right)\left(x+y-4\right)\)
\(=x^2-\left(y^2-8y+16\right)=x^2-\left(y-4\right)^2=\left(x-y+4\right)\left(x+y-4\right)\)