vereinfachen (x-yi)^3

Lösung

vereinfachen

(x - y i)^{3}

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

Schritte zur Lösung

(x - y i)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

x^{3} - 3 x^{2} y i + 3 x (y i)^{2} - (y i)^{3} : x^{3} - 3 x^{2} y i - 3 x y^{2} + y^{3} i

= x^{3} - 3 x^{2} y i - 3 x y^{2} + y^{3} i

Rewrite in standard complex form:

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

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

e x p an d lo g_{10} (x^{3} y^{- 10})

e x p an d \frac{- 1 + 1 - 4 ( - π - 4 πn )}{2}

e x p an d \frac{4}{( x + 2 ) ^{2}}

e x p an d (3 t - 1)^{3} d t

e x p an d \frac{( 6 x + 2 ) ( x ^{3} + 2 x - 7 )}{x ^{6} - 2 x + 7}