de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

erweitern ((a+b)^2-(a-b)^2)^2

Lösung

erweitern

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

Lösung

18 a^{2} b^{2} - 2 b^{2} a^{2}

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

Vereinfache

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

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

Schreibe

(a + b)^{4}

um:

a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4}

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

Schreibe

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

um:

- 2 a^{4} - 2 b^{4} + 6 a^{2} b^{2} - 2 b^{2} a^{2}

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

Schreibe

(a - b)^{4}

um:

a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}

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

Vereinfache

a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} - 2 a^{4} - 2 b^{4} + 6 a^{2} b^{2} - 2 b^{2} a^{2} + a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4} : 18 a^{2} b^{2} - 2 b^{2} a^{2}

= 18 a^{2} b^{2} - 2 b^{2} a^{2}

Beliebte Beispiele

erweitern (3x^2-4x-5)(-2x^2+2x+2)

e x p an d (3 x^{2} - 4 x - 5) (- 2 x^{2} + 2 x + 2)

vereinfachen 50/100

s im pl i f y \frac{50}{100}

vereinfachen \sqrt[4]{20736/1296}

s im pl i f y 4 \frac{20736}{1296}

vereinfachen j*j

s im pl i f y j \cdot j

erweitern 5(2x-1)

e x p an d 5 (2 x - 1)