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Factorizar el polinomio x^8+y^8

Expresión a simplificar:

Solución

Ha introducido [src]
 8    8
x  + y 
$$x^{8} + y^{8}$$
x^8 + y^8
Factorización [src]
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/      /       ___________          ___________\\ /      /     ___________          ___________\\ /      /       ___________          ___________\\ /      /     ___________          ___________\\ |      |  ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  || |      |  ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  || |      |    ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  || |      |  ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  ||
|      |      /       ___          /       ___ || |      |    /       ___          /       ___ || |      |      /       ___          /       ___ || |      |    /       ___          /       ___ || |      |\/ 2 *  /   - + -----    \/ 2 *  /   - - -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- || |      |\/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- || |      |  \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - + -----    I*\/ 2 *  /   - - ----- || |      |\/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- ||
|      |     /  1   \/ 2          /  1   \/ 2  || |      |   /  1   \/ 2          /  1   \/ 2  || |      |     /  1   \/ 2          /  1   \/ 2  || |      |   /  1   \/ 2          /  1   \/ 2  || |      |      \/    2     4            \/    2     4              \/    2     4              \/    2     4   || |      |      \/    2     4            \/    2     4              \/    2     4              \/    2     4   || |      |        \/    2     4            \/    2     4              \/    2     4              \/    2     4   || |      |      \/    2     4            \/    2     4              \/    2     4              \/    2     4   ||
|x - y*|-   /   - - -----  + I*  /   - + ----- ||*|x - y*|  /   - - -----  - I*  /   - + ----- ||*|x - y*|-   /   - + -----  - I*  /   - - ----- ||*|x - y*|  /   - + -----  + I*  /   - - ----- ||*|x - y*|---------------------- - ---------------------- + ------------------------ + ------------------------||*|x - y*|---------------------- + ---------------------- + ------------------------ - ------------------------||*|x - y*|- ---------------------- - ---------------------- + ------------------------ - ------------------------||*|x - y*|---------------------- - ---------------------- - ------------------------ - ------------------------||
\      \  \/    2     4        \/    2     4   // \      \\/    2     4        \/    2     4   // \      \  \/    2     4        \/    2     4   // \      \\/    2     4        \/    2     4   // \      \          2                        2                         2                          2            // \      \          2                        2                         2                          2            // \      \            2                        2                         2                          2            // \      \          2                        2                         2                          2            //
$$\left(x - y \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x - y \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x - y \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x - y \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x - y \left(- \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}\right)\right) \left(x - y \left(\frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2}\right)\right) \left(x - y \left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}\right)\right) \left(x - y \left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2}\right)\right)$$
(((((((x - y*(-sqrt(1/2 - sqrt(2)/4) + i*sqrt(1/2 + sqrt(2)/4)))*(x - y*(sqrt(1/2 - sqrt(2)/4) - i*sqrt(1/2 + sqrt(2)/4))))*(x - y*(-sqrt(1/2 + sqrt(2)/4) - i*sqrt(1/2 - sqrt(2)/4))))*(x - y*(sqrt(1/2 + sqrt(2)/4) + i*sqrt(1/2 - sqrt(2)/4))))*(x - y*(sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2)))*(x - y*(sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2)))*(x - y*(-sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2)))*(x - y*(sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2))
Respuesta numérica [src]
x^8 + y^8
x^8 + y^8