faktorisieren a^3-64b^3c^3

Lösung

faktorisieren

a^{3} - 64 b^{3} c^{3}

(a - 4 b c) (a^{2} + 4 ab c + 16 b^{2} c^{2})

Schritte zur Lösung

a^{3} - 64 b^{3} c^{3}

Schreibe

64 b^{3} c^{3}

um:

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

= a^{3} - (2^{2} b c)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

a^{3} - (2^{2} b c)^{3} = (a - 2^{2} b c) (a^{2} + a 2^{2} b c + (2^{2} b c)^{2})

= (a - 2^{2} b c) (a^{2} + a 2^{2} b c + (2^{2} b c)^{2})

Vereinfache

(a - 2^{2} b c) (a^{2} + a \cdot 2^{2} b c + (2^{2} b c)^{2}) : (a - 4 b c) (a^{2} + 4 ab c + 16 b^{2} c^{2})

= (a - 4 b c) (a^{2} + 4 ab c + 16 b^{2} c^{2})

s im pl i f y [24]

f a c t or (x^{2} + y^{2}) - 50

f a c t or 27 + 33

f a c t or d (ln (a))

f a c t or 4 + 50 i