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Beliebt Algebra >

erweitern (x-a)(x-b)(x-c)(x-d)(x-e)

Lösung

erweitern

(x - a) (x - b) (x - c) (x - d) (x - e)

Lösung

x^{5} - e x^{4} - d x^{4} + e d x^{3} - c x^{4} + ec x^{3} + c d x^{3} - ec d x^{2} - b x^{4} + e b x^{3} + b d x^{3} - e b d x^{2} + b c x^{3} - e b c x^{2} - b c d x^{2} + e b c d x - a x^{4} + e a x^{3} + a d x^{3} - e a d x^{2} + a c x^{3} - e a c x^{2} - a c d x^{2} + e a c d x + ab x^{3} - e ab x^{2} - ab d x^{2} + e ab d x - ab c x^{2} + e ab c x + ab c d x - e ab c d

Schritte zur Lösung

(x - a) (x - b) (x - c) (x - d) (x - e)

Multipliziere aus

(x - a) (x - b) : x^{2} - b x - a x + ab

= (x^{2} - b x - a x + ab) (x - c) (x - d) (x - e)

Multipliziere aus

(x^{2} - b x - a x + ab) (x - c) : x^{3} - c x^{2} - b x^{2} + b c x - a x^{2} + a c x + ab x - ab c

= (x^{3} - c x^{2} - b x^{2} + b c x - a x^{2} + a c x + ab x - ab c) (x - d) (x - e)

Multipliziere aus

(x^{3} - c x^{2} - b x^{2} + b c x - a x^{2} + a c x + ab x - ab c) (x - d) : x^{4} - d x^{3} - c x^{3} + c d x^{2} - b x^{3} + b d x^{2} + b c x^{2} - b c d x - a x^{3} + a d x^{2} + a c x^{2} - a c d x + ab x^{2} - ab d x - ab c x + ab c d

= (x^{4} - d x^{3} - c x^{3} + c d x^{2} - b x^{3} + b d x^{2} + b c x^{2} - b c d x - a x^{3} + a d x^{2} + a c x^{2} - a c d x + ab x^{2} - ab d x - ab c x + ab c d) (x - e)

Multipliziere aus

(x^{4} - d x^{3} - c x^{3} + c d x^{2} - b x^{3} + b d x^{2} + b c x^{2} - b c d x - a x^{3} + a d x^{2} + a c x^{2} - a c d x + ab x^{2} - ab d x - ab c x + ab c d) (x - e) : x^{5} - e x^{4} - d x^{4} + e d x^{3} - c x^{4} + ec x^{3} + c d x^{3} - ec d x^{2} - b x^{4} + e b x^{3} + b d x^{3} - e b d x^{2} + b c x^{3} - e b c x^{2} - b c d x^{2} + e b c d x - a x^{4} + e a x^{3} + a d x^{3} - e a d x^{2} + a c x^{3} - e a c x^{2} - a c d x^{2} + e a c d x + ab x^{3} - e ab x^{2} - ab d x^{2} + e ab d x - ab c x^{2} + e ab c x + ab c d x - e ab c d

= x^{5} - e x^{4} - d x^{4} + e d x^{3} - c x^{4} + ec x^{3} + c d x^{3} - ec d x^{2} - b x^{4} + e b x^{3} + b d x^{3} - e b d x^{2} + b c x^{3} - e b c x^{2} - b c d x^{2} + e b c d x - a x^{4} + e a x^{3} + a d x^{3} - e a d x^{2} + a c x^{3} - e a c x^{2} - a c d x^{2} + e a c d x + ab x^{3} - e ab x^{2} - ab d x^{2} + e ab d x - ab c x^{2} + e ab c x + ab c d x - e ab c d

Beliebte Beispiele

erweitern 1/(2k(4-8k+20k^2))

e x p an d \frac{1}{2 k ( 4 - 8 k + 20 k ^{2} )}

erweitern (2(x+1))!

e x p an d (2 (x + 1))!

erweitern (2+sin(θ))^2

e x p an d (2 + sin (θ))^{2}

erweitern ((4-x)^2)/4

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

erweitern 20000(-(e^{(-x-2)/2}x)/(2)+3e^{-x/2-1})

e x p an d 20000 (- \frac{e ^{\frac{- x - 2}{2}} x}{2} + 3 e^{- \frac{x}{2} - 1})