vereinfachen (5x^2+4yi)^2

Lösung

vereinfachen

(5 x^{2} + 4 y i)^{2}

(25 x^{4} - 16 y^{2}) + 40 x^{2} y i

Schritte zur Lösung

(5 x^{2} + 4 y i)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(5 x^{2} + 4 y i)^{2} = (5 x^{2})^{2} + 2 \cdot 5 x^{2} \cdot 4 y i + (4 y i)^{2}

= (5 x^{2})^{2} + 2 \cdot 5 x^{2} \cdot 4 y i + (4 y i)^{2}

(5 x^{2})^{2} = 25 x^{4}

2 \cdot 5 x^{2} \cdot 4 y i = 40 x^{2} y i

(4 y i)^{2} = - 16 y^{2}

= 25 x^{4} + 40 x^{2} y i - 16 y^{2}

Rewrite in standard complex form:

(25 x^{4} - 16 y^{2}) + 40 x^{2} y i

= (25 x^{4} - 16 y^{2}) + 40 x^{2} y i

e x p an d \frac{2}{( 1 - x ) ^{3}}

e x p an d \frac{1}{x ( x - 2 )}

e x p an d (x - 3) (x + 1 + 2)

s im pl i f y (2 + z i)^{2}

e x p an d (1 + cos (θ))^{3}