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Factorizar el polinomio y*x^2+x*z^2+z*y^2-y*z^2-x*y^2-z*x^2

Expresión a simplificar:

Solución

Ha introducido [src]
   2      2      2      2      2      2
y*x  + x*z  + z*y  - y*z  - x*y  - z*x 
$$- x^{2} z + \left(- x y^{2} + \left(- y z^{2} + \left(y^{2} z + \left(x^{2} y + x z^{2}\right)\right)\right)\right)$$
y*x^2 + x*z^2 + z*y^2 - y*z^2 - x*y^2 - z*x^2
Simplificación general [src]
   2      2      2      2      2      2
x*z  + y*x  + z*y  - x*y  - y*z  - z*x 
$$x^{2} y - x^{2} z - x y^{2} + x z^{2} + y^{2} z - y z^{2}$$
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2
Parte trigonométrica [src]
   2      2      2      2      2      2
x*z  + y*x  + z*y  - x*y  - y*z  - z*x 
$$x^{2} y - x^{2} z - x y^{2} + x z^{2} + y^{2} z - y z^{2}$$
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2
Denominador común [src]
   2      2      2      2      2      2
x*z  + y*x  + z*y  - x*y  - y*z  - z*x 
$$x^{2} y - x^{2} z - x y^{2} + x z^{2} + y^{2} z - y z^{2}$$
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2
Denominador racional [src]
   2      2      2      2      2      2
x*z  + y*x  + z*y  - x*y  - y*z  - z*x 
$$x^{2} y - x^{2} z - x y^{2} + x z^{2} + y^{2} z - y z^{2}$$
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2
Respuesta numérica [src]
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2
Compilar la expresión [src]
   2     / 2    2\     / 2    2\      2
x*z  + y*\x  - z / + z*\y  - x / - x*y 
$$- x y^{2} + x z^{2} + y \left(x^{2} - z^{2}\right) + z \left(- x^{2} + y^{2}\right)$$
   2      2      2      2      2      2
x*z  + y*x  + z*y  - x*y  - y*z  - z*x 
$$x^{2} y - x^{2} z - x y^{2} + x z^{2} + y^{2} z - y z^{2}$$
   2     / 2    2\      2      2      2
x*z  + y*\x  - z / + z*y  - x*y  - z*x 
$$- x^{2} z - x y^{2} + x z^{2} + y^{2} z + y \left(x^{2} - z^{2}\right)$$
  / 2    2\     / 2    2\      2      2
x*\z  - y / + y*\x  - z / + z*y  - z*x 
$$- x^{2} z + x \left(- y^{2} + z^{2}\right) + y^{2} z + y \left(x^{2} - z^{2}\right)$$
   2      2     / 2    2\      2      2
x*z  + y*x  + z*\y  - x / - x*y  - y*z 
$$x^{2} y - x y^{2} + x z^{2} - y z^{2} + z \left(- x^{2} + y^{2}\right)$$
  / 2    2\      2    2              2
x*\z  - y / + z*y  + x *(y - z) - y*z 
$$x^{2} \left(y - z\right) + x \left(- y^{2} + z^{2}\right) + y^{2} z - y z^{2}$$
   2     / 2    2\    2              2
y*x  + z*\y  - x / + z *(x - y) - x*y 
$$x^{2} y - x y^{2} + z^{2} \left(x - y\right) + z \left(- x^{2} + y^{2}\right)$$
   2     / 2    2\    2              2
x*z  + y*\x  - z / + y *(z - x) - z*x 
$$- x^{2} z + x z^{2} + y^{2} \left(- x + z\right) + y \left(x^{2} - z^{2}\right)$$
  / 2    2\      2      2      2      2
x*\z  - y / + y*x  + z*y  - y*z  - z*x 
$$x^{2} y - x^{2} z + x \left(- y^{2} + z^{2}\right) + y^{2} z - y z^{2}$$
  / 2    2\      2     / 2    2\      2
x*\z  - y / + y*x  + z*\y  - x / - y*z 
$$x^{2} y + x \left(- y^{2} + z^{2}\right) - y z^{2} + z \left(- x^{2} + y^{2}\right)$$
x*(z^2 - y^2) + y*x^2 + z*(y^2 - x^2) - y*z^2
Unión de expresiones racionales [src]
  / 2      \      2      2      2      2
x*\z  + x*y/ + z*y  - x*y  - y*z  - z*x 
$$- x^{2} z - x y^{2} + x \left(x y + z^{2}\right) + y^{2} z - y z^{2}$$
x*(z^2 + x*y) + z*y^2 - x*y^2 - y*z^2 - z*x^2
Combinatoria [src]
(x - y)*(x - z)*(y - z)
$$\left(x - y\right) \left(x - z\right) \left(y - z\right)$$
(x - y)*(x - z)*(y - z)
Potencias [src]
   2      2      2      2      2      2
x*z  + y*x  + z*y  - x*y  - y*z  - z*x 
$$x^{2} y - x^{2} z - x y^{2} + x z^{2} + y^{2} z - y z^{2}$$
x*z^2 + y*x^2 + z*y^2 - x*y^2 - y*z^2 - z*x^2