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Factorizar el polinomio y^8-y^3

Expresión a simplificar:

Solución

Ha introducido [src]
 8    3
y  - y 
$$y^{8} - y^{3}$$
y^8 - y^3
Factorización [src]
          /                       ___________\ /                       ___________\ /                       ___________\ /                       ___________\
          |          ___         /       ___ | |          ___         /       ___ | |          ___         /       ___ | |          ___         /       ___ |
          |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  |
x*(x - 1)*|x + - - ----- + I*  /   - + ----- |*|x + - - ----- - I*  /   - + ----- |*|x + - + ----- + I*  /   - - ----- |*|x + - + ----- - I*  /   - - ----- |
          \    4     4       \/    8     8   / \    4     4       \/    8     8   / \    4     4       \/    8     8   / \    4     4       \/    8     8   /
$$x \left(x - 1\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$
((((x*(x - 1))*(x + 1/4 - sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 - sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))
Respuesta numérica [src]
y^8 - y^3
y^8 - y^3
Unión de expresiones racionales [src]
 3 /      5\
y *\-1 + y /
$$y^{3} \left(y^{5} - 1\right)$$
y^3*(-1 + y^5)
Combinatoria [src]
 3          /         2    3    4\
y *(-1 + y)*\1 + y + y  + y  + y /
$$y^{3} \left(y - 1\right) \left(y^{4} + y^{3} + y^{2} + y + 1\right)$$
y^3*(-1 + y)*(1 + y + y^2 + y^3 + y^4)