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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5-y^5

Factorizar el polinomio x^5-y^5

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    5
x  - y
x5−y5x^{5} - y^{5} 
x^5 - y^5
Factorización [src] 
        /      /                     ___________\\ /      /                     ___________\\ /      /                     ___________\\ /      /                     ___________\\
        |      |        ___         /       ___ || |      |        ___         /       ___ || |      |        ___         /       ___ || |      |        ___         /       ___ ||
        |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  ||
(x - y)*|x - y*|- - + ----- - I*  /   - + ----- ||*|x - y*|- - + ----- + I*  /   - + ----- ||*|x - y*|- - - ----- - I*  /   - - ----- ||*|x - y*|- - - ----- + I*  /   - - ----- ||
        \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   //
(x−y)(x−y(−14+54−i58+58))(x−y(−14+54+i58+58))(x−y(−54−14−i58−58))(x−y(−54−14+i58−58))\left(x - y\right) \left(x - y \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x - y \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x - y \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x - y \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) 
((((x - y)*(x - y*(-1/4 + sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8))))*(x - y*(-1/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8))))*(x - y*(-1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))))*(x - y*(-1/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))
Respuesta numérica [src] 
x^5 - y^5
x^5 - y^5
Combinatoria [src] 
        / 4    4      3      3    2  2\
(x - y)*\x  + y  + x*y  + y*x  + x *y /
(x−y)(x4+x3y+x2y2+xy3+y4)\left(x - y\right) \left(x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4}\right) 
(x - y)*(x^4 + y^4 + x*y^3 + y*x^3 + x^2*y^2)
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