vereinfachen (2i+5)(x+iy)^2

Lösung

vereinfachen

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

(5 x^{2} - 4 x y - 5 y^{2}) + (2 x^{2} + 10 x y - 2 y^{2}) i

Schritte zur Lösung

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

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

Schreibe

(x + i y)^{2}

um:

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

= (x^{2} + 2 x y i - y^{2}) (2 i + 5)

Setze Klammern

= x^{2} \cdot 2 i + x^{2} \cdot 5 + 2 x y i 2 i + 2 x y i 5 - y^{2} \cdot 2 i - y^{2} \cdot 5

Vereinfache

x^{2} \cdot 2 i + x^{2} \cdot 5 + 2 x y i 2 i + 2 x y i 5 - y^{2} \cdot 2 i - y^{2} \cdot 5 : 2 x^{2} i + 5 x^{2} - 4 x y + 10 x y i - 2 i y^{2} - 5 y^{2}

= 2 x^{2} i + 5 x^{2} - 4 x y + 10 x y i - 2 i y^{2} - 5 y^{2}

Rewrite in standard complex form:

(5 x^{2} - 4 x y - 5 y^{2}) + (2 x^{2} + 10 x y - 2 y^{2}) i

= (5 x^{2} - 4 x y - 5 y^{2}) + (2 x^{2} + 10 x y - 2 y^{2}) i

e x p an d x^{(\frac{3}{5})} (x - 3)

e x p an d (1 - 5) (2 + 3)

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

s im pl i f y \frac{8 t}{8 t ^{2} + 1} - \frac{2}{2 ( 8 t ^{2} + 1 )}

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