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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 | |    \/  -y     I*\/ 3 *\/  -y  | |    \/  -y     I*\/ 3 *\/  -y  | |    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\|
\x - \/  -y  /*|x + -------- + ----------------|*|x + -------- - ----------------|*|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|----||
               \       2              2        / \       2              2        / \                \9 /                 \9 // \                \9 /                 \9 // \                  \ 9  /                 \ 9  // \                  \ 9  /                 \ 9  // \                  \ 9  /                 \ 9  // \                  \ 9  /                 \ 9  //
(x−−y39)(x+(−y392+3i−y392))(x+(−y392−3i−y392))(x+(−y39cos⁡(π9)+i−y39sin⁡(π9)))(x+(−y39cos⁡(π9)−i−y39sin⁡(π9)))(x+(−−y39cos⁡(2π9)+i−y39sin⁡(2π9)))(x+(−−y39cos⁡(2π9)−i−y39sin⁡(2π9)))(x+(−−y39cos⁡(4π9)+i−y39sin⁡(4π9)))(x+(−−y39cos⁡(4π9)−i−y39sin⁡(4π9)))\left(x - \sqrt[9]{- y^{3}}\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 + \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) 
((((((((x - (-y^3)^(1/9))*(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)*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))
Combinatoria [src] 
/     3\ / 6    2      3\
\y + x /*\x  + y  - y*x /
(x3+y)(x6−x3y+y2)\left(x^{3} + y\right) \left(x^{6} - x^{3} y + y^{2}\right) 
(y + x^3)*(x^6 + y^2 - y*x^3)
Respuesta numérica [src] 
x^9 + y^3
x^9 + y^3
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