Sr Examen
Factorizar el polinomio y^2-y^8
Solución
Factorización
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/ ___\ / ___\ / ___\ / ___\
| 1 I*\/ 3 | | 1 I*\/ 3 | | 1 I*\/ 3 | | 1 I*\/ 3 |
(x + 1)*x*(x - 1)*|x + - + -------|*|x + - - -------|*|x + - - + -------|*|x + - - - -------|
\ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$x \left(x + 1\right) \left(x - 1\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right)$$
((((((x + 1)*x)*(x - 1))*(x + 1/2 + i*sqrt(3)/2))*(x + 1/2 - i*sqrt(3)/2))*(x - 1/2 + i*sqrt(3)/2))*(x - 1/2 - i*sqrt(3)/2)
Combinatoria
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2 / 2\ / 2 \ -y *(1 + y)*(-1 + y)*\1 + y + y /*\1 + y - y/
$$- y^{2} \left(y - 1\right) \left(y + 1\right) \left(y^{2} - y + 1\right) \left(y^{2} + y + 1\right)$$
-y^2*(1 + y)*(-1 + y)*(1 + y + y^2)*(1 + y^2 - y)
Unión de expresiones racionales
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2 / 6\ y *\1 - y /
$$y^{2} \left(1 - y^{6}\right)$$
y^2*(1 - y^6)