factor 8s^3t^6+125q^3

Solución

factor

8 s^{3} t^{6} + 125 q^{3}

(2 s t^{2} + 5 q) (4 s^{2} t^{4} - 10 s t^{2} q + 25 q^{2})

Pasos de solución

8 s^{3} t^{6} + 125 q^{3}

Reescribir

8 s^{3} t^{6}

como

(2 s t^{2})^{3}

Reescribir

125 q^{3}

como

(5 q)^{3}

= (2 s t^{2})^{3} + (5 q)^{3}

Aplicar la siguiente regla de productos notables (Suma de cubos):

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(2 s t^{2})^{3} + (5 q)^{3} = (2 s t^{2} + 5 q) ((2 s t^{2})^{2} - 2 s t^{2} 5 q + (5 q)^{2})

= (2 s t^{2} + 5 q) ((2 s t^{2})^{2} - 2 s t^{2} 5 q + (5 q)^{2})

Simplificar

(2 s t^{2} + 5 q) ((2 s t^{2})^{2} - 2 s t^{2} \cdot 5 q + (5 q)^{2}) : (2 s t^{2} + 5 q) (4 s^{2} t^{4} - 10 s t^{2} q + 25 q^{2})

= (2 s t^{2} + 5 q) (4 s^{2} t^{4} - 10 s t^{2} q + 25 q^{2})