Sr Examen
Factorizar el polinomio x^6-y^9
Solución
Factorización
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/ ____ ____\ / ____ ____\ / ____ ____\ / ____ ____\ | 6 / 9 ___ 6 / 9 | | 6 / 9 ___ 6 / 9 | | 6 / 9 ___ 6 / 9 | | 6 / 9 ___ 6 / 9 | / ____\ / ____\ | \/ y I*\/ 3 *\/ y | | \/ y I*\/ 3 *\/ y | | \/ y I*\/ 3 *\/ y | | \/ y I*\/ 3 *\/ y | | 6 / 9 | | 6 / 9 | |x + ------- + ---------------|*|x + ------- - ---------------|*|x + - ------- + ---------------|*|x + - ------- - ---------------|*\x + \/ y /*\x - \/ y / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{\sqrt[6]{y^{9}}}{2} - \frac{\sqrt{3} i \sqrt[6]{y^{9}}}{2}\right)\right) \left(x + \left(\frac{\sqrt[6]{y^{9}}}{2} + \frac{\sqrt{3} i \sqrt[6]{y^{9}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[6]{y^{9}}}{2} + \frac{\sqrt{3} i \sqrt[6]{y^{9}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[6]{y^{9}}}{2} - \frac{\sqrt{3} i \sqrt[6]{y^{9}}}{2}\right)\right) \left(x + \sqrt[6]{y^{9}}\right) \left(x - \sqrt[6]{y^{9}}\right)$$
(((((x + (y^9)^(1/6)/2 + i*sqrt(3)*(y^9)^(1/6)/2)*(x + (y^9)^(1/6)/2 - i*sqrt(3)*(y^9)^(1/6)/2))*(x - (y^9)^(1/6)/2 + i*sqrt(3)*(y^9)^(1/6)/2))*(x - (y^9)^(1/6)/2 - i*sqrt(3)*(y^9)^(1/6)/2))*(x + (y^9)^(1/6)))*(x - (y^9)^(1/6))
Combinatoria
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/ 2 3\ / 4 6 2 3\ \x - y /*\x + y + x *y /
$$\left(x^{2} - y^{3}\right) \left(x^{4} + x^{2} y^{3} + y^{6}\right)$$
(x^2 - y^3)*(x^4 + y^6 + x^2*y^3)