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