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Factorizar el polinomio m^4-3*m^3*n+m^2*n^2-m^3*n-4*m^2*n^2

Expresión a simplificar:

Solución

Ha introducido [src]
 4      3      2  2    3        2  2
m  - 3*m *n + m *n  - m *n - 4*m *n 
$$- 4 m^{2} n^{2} + \left(- m^{3} n + \left(m^{2} n^{2} + \left(m^{4} - 3 m^{3} n\right)\right)\right)$$
m^4 - 3*m^3*n + m^2*n^2 - m^3*n - 4*m^2*n^2
Simplificación general [src]
 2 / 2      2        \
m *\m  - 3*n  - 4*m*n/
$$m^{2} \left(m^{2} - 4 m n - 3 n^{2}\right)$$
m^2*(m^2 - 3*n^2 - 4*m*n)
Factorización [src]
  /      /      ___\\ /      /      ___\\
m*\m - n*\2 - \/ 7 //*\m - n*\2 + \/ 7 //
$$m \left(m - n \left(2 - \sqrt{7}\right)\right) \left(m - n \left(2 + \sqrt{7}\right)\right)$$
(m*(m - n*(2 - sqrt(7))))*(m - n*(2 + sqrt(7)))
Denominador racional [src]
 4        3      2  2
m  - 4*n*m  - 3*m *n 
$$m^{4} - 4 m^{3} n - 3 m^{2} n^{2}$$
m^4 - 4*n*m^3 - 3*m^2*n^2
Potencias [src]
 4        3      2  2
m  - 4*n*m  - 3*m *n 
$$m^{4} - 4 m^{3} n - 3 m^{2} n^{2}$$
m^4 - 4*n*m^3 - 3*m^2*n^2
Respuesta numérica [src]
m^4 - 4.0*n*m^3 - 3.0*m^2*n^2
m^4 - 4.0*n*m^3 - 3.0*m^2*n^2
Unión de expresiones racionales [src]
 2 /     2                    \
m *\- 3*n  + m*(m - 3*n) - m*n/
$$m^{2} \left(- m n + m \left(m - 3 n\right) - 3 n^{2}\right)$$
m^2*(-3*n^2 + m*(m - 3*n) - m*n)
Parte trigonométrica [src]
 4        3      2  2
m  - 4*n*m  - 3*m *n 
$$m^{4} - 4 m^{3} n - 3 m^{2} n^{2}$$
m^4 - 4*n*m^3 - 3*m^2*n^2
Compilar la expresión [src]
 4        3      2  2
m  - 4*n*m  - 3*m *n 
$$m^{4} - 4 m^{3} n - 3 m^{2} n^{2}$$
m^4 - 4*n*m^3 - 3*m^2*n^2
Combinatoria [src]
 2 / 2      2        \
m *\m  - 3*n  - 4*m*n/
$$m^{2} \left(m^{2} - 4 m n - 3 n^{2}\right)$$
m^2*(m^2 - 3*n^2 - 4*m*n)
Denominador común [src]
 4        3      2  2
m  - 4*n*m  - 3*m *n 
$$m^{4} - 4 m^{3} n - 3 m^{2} n^{2}$$
m^4 - 4*n*m^3 - 3*m^2*n^2