faktorisieren 1+512e^3x^3

Lösung

faktorisieren

1 + 512 e^{3} x^{3}

(8 e x + 1) (64 e^{2} x^{2} - 8 e x + 1)

Schritte zur Lösung

1 + 512 e^{3} x^{3}

Schreibe

512 e^{3} x^{3}

um:

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

= 1 + (2^{3} e x)^{3}

Schreibe

1

um:

1^{3}

= (2^{3} e x)^{3} + 1^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(2^{3} e x)^{3} + 1^{3} = (2^{3} e x + 1) ((2^{3} e x)^{2} - 2^{3} e x + 1)

= (2^{3} e x + 1) ((2^{3} e x)^{2} - 2^{3} e x + 1)

Vereinfache

(2^{3} e x + 1) ((2^{3} e x)^{2} - 2^{3} e x + 1) : (8 e x + 1) (64 e^{2} x^{2} - 8 e x + 1)

= (8 e x + 1) (64 e^{2} x^{2} - 8 e x + 1)

f a c t or sin^{2} (4 t) s h^{2} (2 t)

f a c t or cos (3 x^{2} + 3 x)

f a c t or (x - 1)^{4} + (x - 1)^{2} - 6

f a c t or x (3 t)

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