de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

faktorisieren 27x^{12m}+64y^{9n}

Lösung

faktorisieren

27 x^{12 m} + 64 y^{9 n}

Lösung

(3 x^{4 m} + 4 y^{3 n}) (9 x^{8 m} - 12 x^{4 m} y^{3 n} + 16 y^{6 n})

Schritte zur Lösung

27 x^{12 m} + 64 y^{9 n}

Schreibe

27 x^{12 m}

um:

(3 x^{4 m})^{3}

Schreibe

64 y^{9 n}

um:

(2^{2} y^{3 n})^{3}

= (3 x^{4 m})^{3} + (2^{2} y^{3 n})^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(3 x^{4 m})^{3} + (2^{2} y^{3 n})^{3} = (3 x^{4 m} + 2^{2} y^{3 n}) ((3 x^{4 m})^{2} - 3 x^{4 m} 2^{2} y^{3 n} + (2^{2} y^{3 n})^{2})

= (3 x^{4 m} + 2^{2} y^{3 n}) ((3 x^{4 m})^{2} - 3 x^{4 m} 2^{2} y^{3 n} + (2^{2} y^{3 n})^{2})

Vereinfache

(3 x^{4 m} + 2^{2} y^{3 n}) ((3 x^{4 m})^{2} - 3 x^{4 m} \cdot 2^{2} y^{3 n} + (2^{2} y^{3 n})^{2}) : (3 x^{4 m} + 4 y^{3 n}) (9 x^{8 m} - 12 x^{4 m} y^{3 n} + 16 y^{6 n})

= (3 x^{4 m} + 4 y^{3 n}) (9 x^{8 m} - 12 x^{4 m} y^{3 n} + 16 y^{6 n})

Beliebte Beispiele

faktorisieren 3sin^2(x)-11sin(x)+6

f a c t or 3 sin^{2} (x) - 11 sin (x) + 6

faktorisieren (x-1)^3+(y+3)^3

f a c t or (x - 1)^{3} + (y + 3)^{3}

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

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

faktorisieren (x+y)^6+(x-y)^6

f a c t or (x + y)^{6} + (x - y)^{6}

f(x)=sin(x)(cos(x))^3dx

f (x) = sin (x) (cos (x))^{3} d x