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Simplificación de expresiones/ Descomposición de multiplicadores/ x^9-y^3

Factorizar el polinomio x^9-y^3

Expresión a simplificar:

Solución

Ha introducido [src] 
 9    3
x  - y
x9−y3x^{9} - y^{3} 
x^9 - y^3
Factorización [src] 
                                                                                                                                                                                                                                                                                    /       ____              ____\ /       ____              ____\              
/       ____                ____        \ /       ____                ____        \ /         ____                  ____          \ /         ____                  ____          \ /         ____                  ____          \ /         ____                  ____          \ |    9 /  3        ___ 9 /  3 | |    9 /  3        ___ 9 /  3 | /       ____\
|    9 /  3     /pi\     9 /  3     /pi\| |    9 /  3     /pi\     9 /  3     /pi\| |      9 /  3     /2*pi\     9 /  3     /2*pi\| |      9 /  3     /2*pi\     9 /  3     /2*pi\| |      9 /  3     /4*pi\     9 /  3     /4*pi\| |      9 /  3     /4*pi\     9 /  3     /4*pi\| |    \/  y     I*\/ 3 *\/  y  | |    \/  y     I*\/ 3 *\/  y  | |    9 /  3 |
|x + \/  y  *cos|--| + I*\/  y  *sin|--||*|x + \/  y  *cos|--| - I*\/  y  *sin|--||*|x + - \/  y  *cos|----| + I*\/  y  *sin|----||*|x + - \/  y  *cos|----| - I*\/  y  *sin|----||*|x + - \/  y  *cos|----| + I*\/  y  *sin|----||*|x + - \/  y  *cos|----| - I*\/  y  *sin|----||*|x + ------- + ---------------|*|x + ------- - ---------------|*\x - \/  y  /
\               \9 /                \9 // \               \9 /                \9 // \                 \ 9  /                \ 9  // \                 \ 9  /                \ 9  // \                 \ 9  /                \ 9  // \                 \ 9  /                \ 9  // \       2             2       / \       2             2       /
(x+(y39cos⁡(π9)−iy39sin⁡(π9)))(x+(y39cos⁡(π9)+iy39sin⁡(π9)))(x+(−y39cos⁡(2π9)+iy39sin⁡(2π9)))(x+(−y39cos⁡(2π9)−iy39sin⁡(2π9)))(x+(−y39cos⁡(4π9)+iy39sin⁡(4π9)))(x+(−y39cos⁡(4π9)−iy39sin⁡(4π9)))(x+(y392+3iy392))(x+(y392−3iy392))(x−y39)\left(x + \left(\sqrt[9]{y^{3}} \cos{\left(\frac{\pi}{9} \right)} - i \sqrt[9]{y^{3}} \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(\sqrt[9]{y^{3}} \cos{\left(\frac{\pi}{9} \right)} + i \sqrt[9]{y^{3}} \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(- \sqrt[9]{y^{3}} \cos{\left(\frac{2 \pi}{9} \right)} + i \sqrt[9]{y^{3}} \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(- \sqrt[9]{y^{3}} \cos{\left(\frac{2 \pi}{9} \right)} - i \sqrt[9]{y^{3}} \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(- \sqrt[9]{y^{3}} \cos{\left(\frac{4 \pi}{9} \right)} + i \sqrt[9]{y^{3}} \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(- \sqrt[9]{y^{3}} \cos{\left(\frac{4 \pi}{9} \right)} - i \sqrt[9]{y^{3}} \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(\frac{\sqrt[9]{y^{3}}}{2} + \frac{\sqrt{3} i \sqrt[9]{y^{3}}}{2}\right)\right) \left(x + \left(\frac{\sqrt[9]{y^{3}}}{2} - \frac{\sqrt{3} i \sqrt[9]{y^{3}}}{2}\right)\right) \left(x - \sqrt[9]{y^{3}}\right) 
((((((((x + (y^3)^(1/9)*cos(pi/9) + i*(y^3)^(1/9)*sin(pi/9))*(x + (y^3)^(1/9)*cos(pi/9) - i*(y^3)^(1/9)*sin(pi/9)))*(x - (y^3)^(1/9)*cos(2*pi/9) + i*(y^3)^(1/9)*sin(2*pi/9)))*(x - (y^3)^(1/9)*cos(2*pi/9) - i*(y^3)^(1/9)*sin(2*pi/9)))*(x - (y^3)^(1/9)*cos(4*pi/9) + i*(y^3)^(1/9)*sin(4*pi/9)))*(x - (y^3)^(1/9)*cos(4*pi/9) - i*(y^3)^(1/9)*sin(4*pi/9)))*(x + (y^3)^(1/9)/2 + i*sqrt(3)*(y^3)^(1/9)/2))*(x + (y^3)^(1/9)/2 - i*sqrt(3)*(y^3)^(1/9)/2))*(x - (y^3)^(1/9))
Respuesta numérica [src] 
x^9 - y^3
x^9 - y^3
Combinatoria [src] 
/ 3    \ / 6    2      3\
\x  - y/*\x  + y  + y*x /
(x3−y)(x6+x3y+y2)\left(x^{3} - y\right) \left(x^{6} + x^{3} y + y^{2}\right) 
(x^3 - y)*(x^6 + y^2 + y*x^3)
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