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\(x^4+y^2-2x^2y+x^2+2x-2y\)
\(=\left(y^2-x^2y-xy\right)-\left(x^2y-x^4-x^3\right)+\left(xy-x^3-x^2\right)-\left(2y-2x^2-2x\right)\)
\(=y\left(y-x^2-x\right)-x^2\left(y-x^2-x\right)+x\left(y-x^2-x\right)-2\left(y-x^2-x\right)\)
\(=\left(y-x^2+x-2\right)\left(y-x^2-x\right)\)
x6+x4+x2y2+y4-y6=(x6-y6)+(x4+x2y2+y4)=(x2-y2)(x4+x2y2+y4)+(x4+x2y2+y4)=(x4+x2y2+y4)(x2-y2+1)=((x2+y2)2-x2y2)(x2-y2+1)
=(x2+xy+y2)(x2-xy+y2)(x2-y2+1)
x4-30x2+31x-30=(x4+x)-(30x2-30x+30)=x(x+1)(x2-x+1)-30(x2-x+1)=(x2-x+1)(x2+x-30)=(x2-x+1)(x-5)(x+6)
\(x^2+y^2-x^2y^2+xy-x-y\)
\(\Leftrightarrow x^2\left(1-y\right)\left(1+y\right)-y\left(1-y\right)-x\left(1-y\right)\)
\(\Leftrightarrow\left(1-y\right)\left(x^2+x^2y-y-x\right)\)
\(\Leftrightarrow\left(1-y\right)\left(x+y\right)\left(x-1\right)\left(x+1\right)\)
-[ ((x2)2+(y2)2+(z2)2-2x2y2-2x2z2+2y2z2)-4y2z2]
- ( (x2-y2-z2)2-(2yz)2)
-( x2-y2-z2-2yz )(x2-y2-z2+2yz)
Sai thì bảo mình đừng k sai a -)
\(x^4-2x^2y^2+y^4-1=0\Leftrightarrow\left(x^2-y^2\right)^2-1=0\Leftrightarrow\left(x^2-y^2-1\right).\left(x^2-y^2+1\right)=0\\ \)
\(x^2+2xy+2x+2y+y^2+1=0\Leftrightarrow\left(x+y+1\right)^2=0\)
\(x^4+x^2y^2+y^2\)
\(=x^4+2x^2y^2-x^2y^2+y^2\)
\(=\left(x^4+2x^2y^2+y^2\right)-x^2y^2\)
\(=\left(x^2+y\right)^2-x^2y^2\)
\(=\left(x^2+y-x^2y^2\right)\left(x^2+y+x^2y^2\right)\)