Sr Examen
Factorizar el polinomio b^8-c^8
Solución
Factorización
[src]
/ / ___ ___\\ / / ___ ___\\ / / ___ ___\\ / / ___ ___\\
| | \/ 2 I*\/ 2 || | | \/ 2 I*\/ 2 || | |\/ 2 I*\/ 2 || | |\/ 2 I*\/ 2 ||
(b + c)*(b - c)*(b + I*c)*(b - I*c)*|b - c*|- ----- - -------||*|b - c*|- ----- + -------||*|b - c*|----- - -------||*|b - c*|----- + -------||
\ \ 2 2 // \ \ 2 2 // \ \ 2 2 // \ \ 2 2 //
$$\left(b - c\right) \left(b + c\right) \left(b + i c\right) \left(b - i c\right) \left(b - c \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(b - c \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(b - c \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(b - c \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right)$$
(((((((b + c)*(b - c))*(b + i*c))*(b - i*c))*(b - c*(-sqrt(2)/2 - i*sqrt(2)/2)))*(b - c*(-sqrt(2)/2 + i*sqrt(2)/2)))*(b - c*(sqrt(2)/2 - i*sqrt(2)/2)))*(b - c*(sqrt(2)/2 + i*sqrt(2)/2))
Combinatoria
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/ 2 2\ / 4 4\ (b + c)*(b - c)*\b + c /*\b + c /
$$\left(b - c\right) \left(b + c\right) \left(b^{2} + c^{2}\right) \left(b^{4} + c^{4}\right)$$
(b + c)*(b - c)*(b^2 + c^2)*(b^4 + c^4)