de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

faktorisieren a^3b^6+c^9

Lösung

faktorisieren

a^{3} b^{6} + c^{9}

Lösung

(a b^{2} + c^{3}) (a^{2} b^{4} - a b^{2} c^{3} + c^{6})

Schritte zur Lösung

a^{3} b^{6} + c^{9}

Schreibe

a^{3} b^{6}

um:

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

= (a b^{2})^{3} + c^{9}

Wende Exponentenregel an:

a^{b c} = (a^{b})^{c}

c^{9} = (c^{3})^{3}

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

Wende Formel zur Summe von dritten Potenzen an:

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

(a b^{2})^{3} + (c^{3})^{3} = (a b^{2} + c^{3}) ((a b^{2})^{2} - a b^{2} c^{3} + c^{6})

= (c^{3} + a b^{2}) ((a b^{2})^{2} - c^{3} a b^{2} + c^{6})

Vereinfache

(a b^{2} + c^{3}) ((a b^{2})^{2} - a b^{2} c^{3} + c^{6}) : (a b^{2} + c^{3}) (a^{2} b^{4} - a b^{2} c^{3} + c^{6})

= (a b^{2} + c^{3}) (a^{2} b^{4} - a b^{2} c^{3} + c^{6})

Beliebte Beispiele

faktorisieren (x+4)-x^3-3x^2

f a c t or (x + 4) - x^{3} - 3 x^{2}

faktorisieren (a^2)/4-b^2

f a c t or \frac{a ^{2}}{4} - b^{2}

faktorisieren 3x-9y-xz+3yz

f a c t or 3 x - 9 y - x z + 3 yz

faktorisieren (3a)^2+10ab+(7b)^2

f a c t or (3 a)^{2} + 10 ab + (7 b)^{2}

faktorisieren sin^2(x)-3sin(x)-40

f a c t or sin^{2} (x) - 3 sin (x) - 40