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Simplificación de expresiones/ Descomposición de multiplicadores/ 8*m^7-6*m^2*n-12*m^5*n^3+9*n^4

Factorizar el polinomio 8*m^7-6*m^2*n-12*m^5*n^3+9*n^4

Expresión a simplificar:

Solución

Ha introducido [src] 
   7      2         5  3      4
8*m  - 6*m *n - 12*m *n  + 9*n
9n4+(−12m5n3+(8m7−6m2n))9 n^{4} + \left(- 12 m^{5} n^{3} + \left(8 m^{7} - 6 m^{2} n\right)\right) 
8*m^7 - 6*m^2*n - 12*m^5*n^3 + 9*n^4
Simplificación general [src] 
   7      4       5  3        2
8*m  + 9*n  - 12*m *n  - 6*n*m
8m7−12m5n3−6m2n+9n48 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4} 
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Factorización [src] 
                                                               /                                                                        ___________\ /                                                                        ___________\ /                                                                        ___________\ /                                                                        ___________\
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/             ____\ /             ____\                        |                                                   3/5 5 ___ 5 ___    /  5   \/ 5  | |                                                   3/5 5 ___ 5 ___    /  5   \/ 5  | |                                                   3/5 5 ___ 5 ___    /  5   \/ 5  | |                                                   3/5 5 ___ 5 ___    /  5   \/ 5  |
|      ___   /  3 | |      ___   /  3 | /     3/5 5 ___ 5 ___\ |     3/5 5 ___ 5 ___    3/5 5 ___   ___ 5 ___   I*2   *\/ 3 *\/ n *  /   - + ----- | |     3/5 5 ___ 5 ___    3/5 5 ___   ___ 5 ___   I*2   *\/ 3 *\/ n *  /   - + ----- | |     3/5 5 ___ 5 ___    3/5 5 ___   ___ 5 ___   I*2   *\/ 3 *\/ n *  /   - - ----- | |     3/5 5 ___ 5 ___    3/5 5 ___   ___ 5 ___   I*2   *\/ 3 *\/ n *  /   - - ----- |
|    \/ 6 *\/  n  | |    \/ 6 *\/  n  | |    2   *\/ 3 *\/ n | |    2   *\/ 3 *\/ n    2   *\/ 3 *\/ 5 *\/ n                       \/    8     8   | |    2   *\/ 3 *\/ n    2   *\/ 3 *\/ 5 *\/ n                       \/    8     8   | |    2   *\/ 3 *\/ n    2   *\/ 3 *\/ 5 *\/ n                       \/    8     8   | |    2   *\/ 3 *\/ n    2   *\/ 3 *\/ 5 *\/ n                       \/    8     8   |
|m + -------------|*|m - -------------|*|m - ----------------|*|m + ---------------- - ---------------------- + -----------------------------------|*|m + ---------------- - ---------------------- - -----------------------------------|*|m + ---------------- + ---------------------- + -----------------------------------|*|m + ---------------- + ---------------------- - -----------------------------------|
\          2      / \          2      / \           2        / \           8                     8                               2                 / \           8                     8                               2                 / \           8                     8                               2                 / \           8                     8                               2                 /
(m−6n32)(m+6n32)(m−23535n52)(m+(−235355n58+23535n58+23535in558+582))(m+(−235355n58+23535n58−23535in558+582))(m+(23535n58+235355n58+23535in558−582))(m+(23535n58+235355n58−23535in558−582))\left(m - \frac{\sqrt{6} \sqrt{n^{3}}}{2}\right) \left(m + \frac{\sqrt{6} \sqrt{n^{3}}}{2}\right) \left(m - \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{2}\right) \left(m + \left(- \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(m + \left(- \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} - \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(m + \left(\frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(m + \left(\frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} - \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) 
((((((m + sqrt(6)*sqrt(n^3)/2)*(m - sqrt(6)*sqrt(n^3)/2))*(m - 2^(3/5)*3^(1/5)*n^(1/5)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 - 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 + i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 + sqrt(5)/8)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 - 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 - i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 + sqrt(5)/8)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 + 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 + i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 - sqrt(5)/8)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 + 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 - i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 - sqrt(5)/8)/2)
Denominador común [src] 
   7      4       5  3        2
8*m  + 9*n  - 12*m *n  - 6*n*m
8m7−12m5n3−6m2n+9n48 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4} 
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Respuesta numérica [src] 
8.0*m^7 + 9.0*n^4 - 6.0*n*m^2 - 12.0*m^5*n^3
8.0*m^7 + 9.0*n^4 - 6.0*n*m^2 - 12.0*m^5*n^3
Combinatoria [src] 
/          5\ /     3      2\
\-3*n + 4*m /*\- 3*n  + 2*m /
(2m2−3n3)(4m5−3n)\left(2 m^{2} - 3 n^{3}\right) \left(4 m^{5} - 3 n\right) 
(-3*n + 4*m^5)*(-3*n^3 + 2*m^2)
Unión de expresiones racionales [src] 
   4      2 /          5      3  3\
9*n  + 2*m *\-3*n + 4*m  - 6*m *n /
2m2(4m5−6m3n3−3n)+9n42 m^{2} \left(4 m^{5} - 6 m^{3} n^{3} - 3 n\right) + 9 n^{4} 
9*n^4 + 2*m^2*(-3*n + 4*m^5 - 6*m^3*n^3)
Parte trigonométrica [src] 
   7      4       5  3        2
8*m  + 9*n  - 12*m *n  - 6*n*m
8m7−12m5n3−6m2n+9n48 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4} 
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Compilar la expresión [src] 
   7      4       5  3        2
8*m  + 9*n  - 12*m *n  - 6*n*m
8m7−12m5n3−6m2n+9n48 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4} 
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Denominador racional [src] 
   7      4       5  3        2
8*m  + 9*n  - 12*m *n  - 6*n*m
8m7−12m5n3−6m2n+9n48 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4} 
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Potencias [src] 
   7      4       5  3        2
8*m  + 9*n  - 12*m *n  - 6*n*m
8m7−12m5n3−6m2n+9n48 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4} 
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
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