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Simplificación de expresiones/ Descomposición de multiplicadores/ m^4+m^2*n^2+n^4

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

Expresión a simplificar:

Solución

Ha introducido [src] 
 4    2  2    4
m  + m *n  + n
$$n^{4} + \left(m^{4} + m^{2} n^{2}\right)$$ 
m^4 + m^2*n^2 + n^4
Simplificación general [src] 
 4    4    2  2
m  + n  + m *n
$$m^{4} + m^{2} n^{2} + n^{4}$$ 
m^4 + n^4 + m^2*n^2
Factorización [src] 
/      /          ___\\ /      /          ___\\ /      /        ___\\ /      /        ___\\
|      |  1   I*\/ 3 || |      |  1   I*\/ 3 || |      |1   I*\/ 3 || |      |1   I*\/ 3 ||
|m - n*|- - - -------||*|m - n*|- - + -------||*|m - n*|- - -------||*|m - n*|- + -------||
\      \  2      2   // \      \  2      2   // \      \2      2   // \      \2      2   //
$$\left(m - n \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(m - n \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(m - n \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(m - n \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right)$$ 
(((m - n*(-1/2 - i*sqrt(3)/2))*(m - n*(-1/2 + i*sqrt(3)/2)))*(m - n*(1/2 - i*sqrt(3)/2)))*(m - n*(1/2 + i*sqrt(3)/2))
Denominador común [src] 
 4    4    2  2
m  + n  + m *n
$$m^{4} + m^{2} n^{2} + n^{4}$$ 
m^4 + n^4 + m^2*n^2
Compilar la expresión [src] 
 4    4    2  2
m  + n  + m *n
$$m^{4} + m^{2} n^{2} + n^{4}$$ 
m^4 + n^4 + m^2*n^2
Respuesta numérica [src] 
m^4 + n^4 + m^2*n^2
m^4 + n^4 + m^2*n^2
Potencias [src] 
 4    4    2  2
m  + n  + m *n
$$m^{4} + m^{2} n^{2} + n^{4}$$ 
m^4 + n^4 + m^2*n^2
Parte trigonométrica [src] 
 4    4    2  2
m  + n  + m *n
$$m^{4} + m^{2} n^{2} + n^{4}$$ 
m^4 + n^4 + m^2*n^2
Unión de expresiones racionales [src] 
 4    2 / 2    2\
n  + m *\m  + n /
$$m^{2} \left(m^{2} + n^{2}\right) + n^{4}$$ 
n^4 + m^2*(m^2 + n^2)
Denominador racional [src] 
 4    4    2  2
m  + n  + m *n
$$m^{4} + m^{2} n^{2} + n^{4}$$ 
m^4 + n^4 + m^2*n^2
Combinatoria [src] 
/ 2    2      \ / 2    2      \
\m  + n  + m*n/*\m  + n  - m*n/
$$\left(m^{2} - m n + n^{2}\right) \left(m^{2} + m n + n^{2}\right)$$ 
(m^2 + n^2 + m*n)*(m^2 + n^2 - m*n)
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