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Simplificación de expresiones/ Descomposición de multiplicadores/ a^4+a^3*b+a^2*b^2+a*b^3+b^4

Factorizar el polinomio a^4+a^3*b+a^2*b^2+a*b^3+b^4

Expresión a simplificar:

Solución

Ha introducido [src] 
 4    3      2  2      3    4
a  + a *b + a *b  + a*b  + b
$$b^{4} + \left(a b^{3} + \left(a^{2} b^{2} + \left(a^{4} + a^{3} b\right)\right)\right)$$ 
a^4 + a^3*b + a^2*b^2 + a*b^3 + b^4
Simplificación general [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Factorización [src] 
/      /                     ___________\\ /      /                     ___________\\ /      /                     ___________\\ /      /                     ___________\\
|      |        ___         /       ___ || |      |        ___         /       ___ || |      |        ___         /       ___ || |      |        ___         /       ___ ||
|      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  || |      |  1   \/ 5         /  5   \/ 5  ||
|a - b*|- - + ----- - I*  /   - + ----- ||*|a - b*|- - + ----- + I*  /   - + ----- ||*|a - b*|- - - ----- - I*  /   - - ----- ||*|a - b*|- - - ----- + I*  /   - - ----- ||
\      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   // \      \  4     4       \/    8     8   //
$$\left(a - b \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a - b \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a - b \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(a - b \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$ 
(((a - b*(-1/4 + sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(a - b*(-1/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8))))*(a - b*(-1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))))*(a - b*(-1/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))
Respuesta numérica [src] 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Potencias [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Denominador racional [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Denominador común [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Combinatoria [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Unión de expresiones racionales [src] 
 4     / 3     / 2            \\
b  + a*\b  + a*\b  + a*(a + b)//
$$a \left(a \left(a \left(a + b\right) + b^{2}\right) + b^{3}\right) + b^{4}$$ 
b^4 + a*(b^3 + a*(b^2 + a*(a + b)))
Parte trigonométrica [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
Compilar la expresión [src] 
 4    4      3      3    2  2
a  + b  + a*b  + b*a  + a *b
$$a^{4} + a^{3} b + a^{2} b^{2} + a b^{3} + b^{4}$$ 
a^4 + b^4 + a*b^3 + b*a^3 + a^2*b^2
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