Sr Examen
Factorizar el polinomio x^5+y^5+x^2*y^3+x^3*y^2
Solución
Ha introducido
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{3} y^{2} + \left(x^{2} y^{3} + \left(x^{5} + y^{5}\right)\right)$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Simplificación general
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Factorización
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/ / ___\\ / / ___\\
| |1 I*\/ 3 || | |1 I*\/ 3 ||
(x + y)*(x + I*y)*(x - I*y)*|x - y*|- - -------||*|x - y*|- + -------||
\ \2 2 // \ \2 2 //
$$\left(x + y\right) \left(x + i y\right) \left(x - i y\right) \left(x - y \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x - y \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right)$$
((((x + y)*(x + i*y))*(x - i*y))*(x - y*(1/2 - i*sqrt(3)/2)))*(x - y*(1/2 + i*sqrt(3)/2))
Denominador común
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Parte trigonométrica
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Compilar la expresión
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Combinatoria
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/ 2 2\ / 2 2 \ (x + y)*\x + y /*\x + y - x*y/
$$\left(x + y\right) \left(x^{2} + y^{2}\right) \left(x^{2} - x y + y^{2}\right)$$
(x + y)*(x^2 + y^2)*(x^2 + y^2 - x*y)
Denominador racional
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Unión de expresiones racionales
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2
Potencias
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5 5 2 3 3 2 x + y + x *y + x *y
$$x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5}$$
x^5 + y^5 + x^2*y^3 + x^3*y^2