factor 8d^3+27c^3e^6

Solución

factor

8 d^{3} + 27 c^{3} e^{6}

(2 d + 3 e^{2} c) (4 d^{2} - 6 e^{2} d c + 9 e^{4} c^{2})

Pasos de solución

8 d^{3} + 27 c^{3} e^{6}

Reescribir

8 d^{3}

como

(2 d)^{3}

Reescribir

27 c^{3} e^{6}

como

(3 c e^{2})^{3}

= (2 d)^{3} + (3 c e^{2})^{3}

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

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

(2 d)^{3} + (3 c e^{2})^{3} = (2 d + 3 c e^{2}) ((2 d)^{2} - 3 c e^{2} 2 d + (3 c e^{2})^{2})

= (3 c e^{2} + 2 d) ((3 c e^{2})^{2} - 3 c e^{2} 2 d + (2 d)^{2})

Simplificar

(2 d + 3 c e^{2}) ((2 d)^{2} - 3 c e^{2} \cdot 2 d + (3 c e^{2})^{2}) : (2 d + 3 e^{2} c) (4 d^{2} - 6 e^{2} d c + 9 e^{4} c^{2})

= (2 d + 3 e^{2} c) (4 d^{2} - 6 e^{2} d c + 9 e^{4} c^{2})

s im pl i f y (25)^{513}

f a c t or 2 sin^{2} (θ) + 5 sin (θ) - 3

s im pl i f y [- 2.7]

f a c t or 2 y^{- 1} + 11 y^{- 4}

f a c t or 2 (a + b)^{2} + 3 (a + b) - 2