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Factorizar el polinomio m^3*n^3-1

Expresión a simplificar:

Solución

Ha introducido [src]
 3  3    
m *n  - 1
$$m^{3} n^{3} - 1$$
m^3*n^3 - 1
Factorización [src]
        /              ___\ /              ___\
        |      1   I*\/ 3 | |      1   I*\/ 3 |
        |    - - - -------| |    - - + -------|
/    1\ |      2      2   | |      2      2   |
|m - -|*|m - -------------|*|m - -------------|
\    n/ \          n      / \          n      /
$$\left(m - \frac{1}{n}\right) \left(m - \frac{- \frac{1}{2} - \frac{\sqrt{3} i}{2}}{n}\right) \left(m - \frac{- \frac{1}{2} + \frac{\sqrt{3} i}{2}}{n}\right)$$
((m - 1/n)*(m - (-1/2 - i*sqrt(3)/2)/n))*(m - (-1/2 + i*sqrt(3)/2)/n)
Respuesta numérica [src]
-1.0 + m^3*n^3
-1.0 + m^3*n^3
Combinatoria [src]
           /           2  2\
(-1 + m*n)*\1 + m*n + m *n /
$$\left(m n - 1\right) \left(m^{2} n^{2} + m n + 1\right)$$
(-1 + m*n)*(1 + m*n + m^2*n^2)