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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5+y^5+x^2*y^3+x^3*y^2

Factorizar el polinomio x^5+y^5+x^2*y^3+x^3*y^2

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x3y2+(x2y3+(x5+y5))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 [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5} 
x^5 + y^5 + x^2*y^3 + x^3*y^2
Factorización [src] 
                            /      /        ___\\ /      /        ___\\
                            |      |1   I*\/ 3 || |      |1   I*\/ 3 ||
(x + y)*(x + I*y)*(x - I*y)*|x - y*|- - -------||*|x - y*|- + -------||
                            \      \2      2   // \      \2      2   //
(x+y)(x+iy)(x−iy)(x−y(12−3i2))(x−y(12+3i2))\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 [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{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 [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{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 [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5} 
x^5 + y^5 + x^2*y^3 + x^3*y^2
Combinatoria [src] 
        / 2    2\ / 2    2      \
(x + y)*\x  + y /*\x  + y  - x*y/
(x+y)(x2+y2)(x2−xy+y2)\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)
Respuesta numérica [src] 
x^5 + y^5 + x^2*y^3 + x^3*y^2
x^5 + y^5 + x^2*y^3 + x^3*y^2
Denominador racional [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{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 [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5} 
x^5 + y^5 + x^2*y^3 + x^3*y^2
Potencias [src] 
 5    5    2  3    3  2
x  + y  + x *y  + x *y
x5+x3y2+x2y3+y5x^{5} + x^{3} y^{2} + x^{2} y^{3} + y^{5} 
x^5 + y^5 + x^2*y^3 + x^3*y^2
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