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