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Simplificación de expresiones/ Descomposición de multiplicadores/ y^6+6*y^3*t^2+9*t^4

Factorizar el polinomio y^6+6*y^3*t^2+9*t^4

Expresión a simplificar:

Solución

Ha introducido [src] 
 6      3  2      4
y  + 6*y *t  + 9*t
$$9 t^{4} + \left(t^{2} \cdot 6 y^{3} + y^{6}\right)$$ 
y^6 + (6*y^3)*t^2 + 9*t^4
Factorización [src] 
/             _____\ /             _____\
|      ___   /   3 | |      ___   /   3 |
|    \/ 3 *\/  -y  | |    \/ 3 *\/  -y  |
|t + --------------|*|t - --------------|
\          3       / \          3       /
$$\left(t - \frac{\sqrt{3} \sqrt{- y^{3}}}{3}\right) \left(t + \frac{\sqrt{3} \sqrt{- y^{3}}}{3}\right)$$ 
(t + sqrt(3)*sqrt(-y^3)/3)*(t - sqrt(3)*sqrt(-y^3)/3)
Simplificación general [src] 
 6      4      2  3
y  + 9*t  + 6*t *y
$$9 t^{4} + 6 t^{2} y^{3} + y^{6}$$ 
y^6 + 9*t^4 + 6*t^2*y^3
Respuesta numérica [src] 
y^6 + 9.0*t^4 + 6.0*t^2*y^3
y^6 + 9.0*t^4 + 6.0*t^2*y^3
Compilar la expresión [src] 
 6      4      2  3
y  + 9*t  + 6*t *y
$$9 t^{4} + 6 t^{2} y^{3} + y^{6}$$ 
y^6 + 9*t^4 + 6*t^2*y^3
Denominador racional [src] 
 6      4      2  3
y  + 9*t  + 6*t *y
$$9 t^{4} + 6 t^{2} y^{3} + y^{6}$$ 
y^6 + 9*t^4 + 6*t^2*y^3
Denominador común [src] 
 6      4      2  3
y  + 9*t  + 6*t *y
$$9 t^{4} + 6 t^{2} y^{3} + y^{6}$$ 
y^6 + 9*t^4 + 6*t^2*y^3
Parte trigonométrica [src] 
 6      4      2  3
y  + 9*t  + 6*t *y
$$9 t^{4} + 6 t^{2} y^{3} + y^{6}$$ 
y^6 + 9*t^4 + 6*t^2*y^3
Combinatoria [src] 
           2
/ 3      2\ 
\y  + 3*t /
$$\left(3 t^{2} + y^{3}\right)^{2}$$ 
(y^3 + 3*t^2)^2
Unión de expresiones racionales [src] 
   4    3 / 3      2\
9*t  + y *\y  + 6*t /
$$9 t^{4} + y^{3} \left(6 t^{2} + y^{3}\right)$$ 
9*t^4 + y^3*(y^3 + 6*t^2)
Potencias [src] 
 6      4      2  3
y  + 9*t  + 6*t *y
$$9 t^{4} + 6 t^{2} y^{3} + y^{6}$$ 
y^6 + 9*t^4 + 6*t^2*y^3
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