erweitern (x-5)(x-5)(x-2i)(x+2i)

Lösung

erweitern

(x - 5) (x - 5) (x - 2 i) (x + 2 i)

x^{4} - 10 x^{3} + 29 x^{2} - 40 x + 100

Schritte zur Lösung

(x - 5) (x - 5) (x - 2 i) (x + 2 i)

Schreibe

(x - 5) (x - 5) (x - 2 i) (x + 2 i)

um:

(x - 5) (x - 5) (x^{2} + 4)

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

Apply FOIL method

(x - 5) (x - 5) : x^{2} - 10 x + 25

= (x^{2} - 10 x + 25) (x^{2} + 4)

Setze Klammern

= x^{2} x^{2} + x^{2} \cdot 4 - 10 x x^{2} - 10 x \cdot 4 + 25 x^{2} + 25 \cdot 4

Vereinfache

x^{2} x^{2} + x^{2} \cdot 4 - 10 x x^{2} - 10 x \cdot 4 + 25 x^{2} + 25 \cdot 4 : x^{4} - 10 x^{3} + 29 x^{2} - 40 x + 100

= x^{4} - 10 x^{3} + 29 x^{2} - 40 x + 100

e x p an d \frac{14 x - 7 h}{x ^{2} ( x + h ) ^{2}}

e x p an d (\frac{1 + 5}{2})^{3}

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

e x p an d \frac{e ^{- x} - x ^{2} - x + 10}{( x - 1 ) ( x + 4 ) ( x - 2 )}

e x p an d (x + sin (\frac{π \cdot x}{2})) \cdot (x + cos (\frac{π \cdot x}{2}))^{2}