Ta có :
\(1)\left(x^2+y^2-5\right)-4x^2y^2-16xy-16\)
\(=\left(x^2+y^2-5\right)^2-[\left(2xy\right)^2+2.2xy.4+4^2]\)
\(=\left(x^2+y^2-5\right)^2-\left(2xy+4\right)^2\)
\(=\left(x^2+y^2-5-2xy-4\right)\left(x^2+y^2-5+2xy+4\right)\)
\(=\left(x^2+y^2-2xy-9\right)\left(x^2+y^2+2xy-1\right)\)
\(=\left[\left(x-y\right)^2-3^2\right]\left[\left(x+y\right)^2-1\right]\)
\(=\left(x-y+3\right)\left(x-y-3\right)\left(x+y-1\right)\left(x+y+1\right)\)
\(2)x^2y^2\left(y-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(y-z+z-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(y-z\right)+x^2y^2\left(z-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=\left(y-z\right)\left(x^2y^2-y^2z^2\right)+\left(z-x\right)\left(x^2y^2-z^2x^2\right)\)
\(=\left(y-z\right)\left(xy-yz\right)\left(xy+yz\right)+\left(z-x\right)\left(xy-zx\right)\left(xy+xz\right)\)
\(=y^2\left(y-z\right)\left(x-z\right)\left(x+z\right)+x^2\left(z-x\right)\left(y-z\right)\left(y+z\right)\)
\(=\left(y-z\right)\left(x-z\right)[y^2\left(x+z\right)-x^2\left(y+z\right)]\)
\(=\left(y-z\right)\left(x-z\right)(y^2x+y^2z-x^2y-x^2z)\)
\(=\left(y-z\right)\left(x-z\right)[(y^2x-x^2y)+(y^2z-x^2z)]\)
\(=\left(y-z\right)\left(x-z\right)[xy(y-x)+z(y^2-x^2)]\)
\(=\left(y-z\right)\left(x-z\right)[xy(y-x)+z(y-x)\left(x+y\right)]\)
\(=\left(y-z\right)\left(x-z\right)(y-x)\left(xy+xz+yz\right)\)
