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