faktorisieren (a+b)^3-1000c^3

Lösung

faktorisieren

(a + b)^{3} - 1000 c^{3}

(a + b - 10 c) ((a + b)^{2} + 10 c (a + b) + 100 c^{2})

Schritte zur Lösung

(a + b)^{3} - 1000 c^{3}

Schreibe

(a + b)^{3} - 1000 c^{3}

um:

(a + b)^{3} - (10 c)^{3}

= (a + b)^{3} - (10 c)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(a + b)^{3} - (10 c)^{3} = ((a + b) - 10 c) ((a + b)^{2} + 10 (a + b) c + 1 0^{2} c^{2})

= ((a + b) - 10 c) ((a + b)^{2} + 10 c (a + b) + 1 0^{2} c^{2})

Fasse zusammen

= (a + b - 10 c) (100 c^{2} + 10 c (a + b) + (a + b)^{2})

f a c t or x^{6} + 6 x^{4} + 12 x^{2} + 8

f a c t or e^{2} - e

f a c t or \cdot (- 3)

f a c t or sin^{3} (x) - cos^{3} (x)

s im pl i f y [5.9]