faktorisieren 8e^3f^6-125g^3

Lösung

faktorisieren

8 e^{3} f^{6} - 125 g^{3}

(2 e f^{2} - 5 g) (4 e^{2} f^{4} + 10 e f^{2} g + 25 g^{2})

Schritte zur Lösung

8 e^{3} f^{6} - 125 g^{3}

Schreibe

8 e^{3} f^{6}

um:

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

Schreibe

125 g^{3}

um:

(5 g)^{3}

= (2 e f^{2})^{3} - (5 g)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(2 e f^{2})^{3} - (5 g)^{3} = (2 e f^{2} - 5 g) ((2 e f^{2})^{2} + 2 e f^{2} 5 g + (5 g)^{2})

= (2 e f^{2} - 5 g) ((2 e f^{2})^{2} + 2 e f^{2} 5 g + (5 g)^{2})

Vereinfache

(2 e f^{2} - 5 g) ((2 e f^{2})^{2} + 2 e f^{2} \cdot 5 g + (5 g)^{2}) : (2 e f^{2} - 5 g) (4 e^{2} f^{4} + 10 e f^{2} g + 25 g^{2})

= (2 e f^{2} - 5 g) (4 e^{2} f^{4} + 10 e f^{2} g + 25 g^{2})

f (x) = (cos (11 x))^{2}

f a c t or e^{5} - e^{3}

f a c t or r (24 π)

f a c t or + (- 5)

f a c t or cos^{6} (θ) + sin^{6} (θ)