erweitern |(1-u^2+v^2)|^2+4u^2v^2+4u^2

Lösung

erweitern

(1 - u^{2} + v^{2})^{2} + 4 u^{2} v^{2} + 4 u^{2}

u^{4} + 2 u^{2} v^{2} + 2 u^{2} + v^{4} + 2 v^{2} + 1

Schritte zur Lösung

1 - u^{2} + v^{2}^{2} + 4 u^{2} v^{2} + 4 u^{2}

Wende Absoluteregel an:

∣ x ∣^{2} = x^{2},

angenommen

x \in R

1 - u^{2} + v^{2}^{2} = (1 - u^{2} + v^{2})^{2}

= (v^{2} + 1 - u^{2})^{2} + 4 u^{2} v^{2} + 4 u^{2}

Vereinfache

= u^{4} + 2 u^{2} v^{2} + 2 u^{2} + v^{4} + 2 v^{2} + 1

e x p an d \frac{191700 ( e + 1 ) ( e - 1 )}{e ^{4}}

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

e x p an d (2 - e^{- 2 x})^{2}

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

e x p an d \frac{ab}{( s ^{2} + a ^{2} ) ( s ^{2} + b ^{2} )}