faktorisieren 343a^3b^3-512c^3

Lösung

faktorisieren

343 a^{3} b^{3} - 512 c^{3}

(7 ab - 8 c) (49 a^{2} b^{2} + 56 ab c + 64 c^{2})

Schritte zur Lösung

343 a^{3} b^{3} - 512 c^{3}

Schreibe

343 a^{3} b^{3}

um:

(7 ab)^{3}

Schreibe

512 c^{3}

um:

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

= (7 ab)^{3} - (2^{3} c)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(7 ab)^{3} - (2^{3} c)^{3} = (7 ab - 2^{3} c) ((7 ab)^{2} + 7 ab 2^{3} c + (2^{3} c)^{2})

= (7 ab - 2^{3} c) ((7 ab)^{2} + 7 ab 2^{3} c + (2^{3} c)^{2})

Vereinfache

(7 ab - 2^{3} c) ((7 ab)^{2} + 7 ab \cdot 2^{3} c + (2^{3} c)^{2}) : (7 ab - 8 c) (49 a^{2} b^{2} + 56 ab c + 64 c^{2})

= (7 ab - 8 c) (49 a^{2} b^{2} + 56 ab c + 64 c^{2})

\frac{d}{d x} (- 2 x^{2} y + y^{2})

s im pl i f y A (2.1)

f a c t or 12 x^{2} y - 3 x + 4 x - 1

f (x) = 1 + 3 (cos (3 x))^{2}

f a c t or 4 x - 4 x