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\(1)\left(x^2+y^2-5\right)-4x^2y^2-16xy-16\)
\(=\left(x^2+y^2-5\right)^2-[\left(2xy\right)^2+2.2xy.4+4^2]\)
\(=\left(x^2+y^2-5\right)^2-\left(2xy+4\right)^2\)
\(=\left(x^2+y^2-5-2xy-4\right)\left(x^2+y^2-5+2xy+4\right)\)
\(=\left(x^2+y^2-2xy-9\right)\left(x^2+y^2+2xy-1\right)\)
\(=\left[\left(x-y\right)^2-3^2\right]\left[\left(x+y\right)^2-1\right]\)
\(=\left(x-y+3\right)\left(x-y-3\right)\left(x+y-1\right)\left(x+y+1\right)\)
\(2)x^2y^2\left(y-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(y-z+z-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(y-z\right)+x^2y^2\left(z-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)
\(=\left(y-z\right)\left(x^2y^2-y^2z^2\right)+\left(z-x\right)\left(x^2y^2-z^2x^2\right)\)
\(=\left(y-z\right)\left(xy-yz\right)\left(xy+yz\right)+\left(z-x\right)\left(xy-zx\right)\left(xy+xz\right)\)
\(=y^2\left(y-z\right)\left(x-z\right)\left(x+z\right)+x^2\left(z-x\right)\left(y-z\right)\left(y+z\right)\)
\(=\left(y-z\right)\left(x-z\right)[y^2\left(x+z\right)-x^2\left(y+z\right)]\)
\(=\left(y-z\right)\left(x-z\right)(y^2x+y^2z-x^2y-x^2z)\)
\(=\left(y-z\right)\left(x-z\right)[(y^2x-x^2y)+(y^2z-x^2z)]\)
\(=\left(y-z\right)\left(x-z\right)[xy(y-x)+z(y^2-x^2)]\)
\(=\left(y-z\right)\left(x-z\right)[xy(y-x)+z(y-x)\left(x+y\right)]\)
\(=\left(y-z\right)\left(x-z\right)(y-x)\left(xy+xz+yz\right)\)
x4 - 5x2 +4
=x4 -4x -x +4
=(x4 - 4x) - (x-4)
=x3(x-4)-(x -4)
=(x3 -1).(x-4)
3, x3 - x + y3 - y
=( x3 + y3) - (x + y)
=(x +y)(x2 - xy +y2) -(x +y)
= x2 - xy + y2
4, x3 - 3x2 -4x +12
= (x3 - 3x2)-(4x -12)
=x2(x - 3) - 4(x - 3)
= (x2 - 4)(x -3)
=(x-2)(x+2)(x-3)
7, 45 +x3 - 5x2 - 9x
=( x3 - 5x2 )-( 9x - 45)
= x2(x-5)-9(x-5)
=( x2- 9)(x-5)
= (x-3)(x+3)(x-5)
\(b,9x^2+90x+225-\left(x-y\right)^2\)
\(=\left(3x+15\right)^2-\left(x-y\right)^2\)
\(=\left(3x+15-x+y\right)\left(3x+15+x-y\right)\)
\(=\left(2x+y+15\right)\left(4x-y+15\right)\)
x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz
=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2
=xy(x+y+z)+zx(x+y+z)+yz(y+z)
=x(y+z)(x+y+z)+yz(y+z)
=(y+z)(x^2+xy+zx+yz)
=(x+y)(y+z)(z+x)
t i c k mk nha!!! 565464556756768768787669789789776575656767676945645645654
X^2-x-6
= x^2-2x.3+3^2
=(x-3)^2