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Beliebt Algebra >

erweitern (sqrt(x)+1)(sqrt(x)-1)^5

Lösung

erweitern

(x + 1) (x - 1)^{5}

Lösung

x^{3} - 4 x^{2} x + 5 x^{2} - 5 x + 4 x - 1

Schritte zur Lösung

(x + 1) (x - 1)^{5}

= (x - 1)^{5} (x + 1)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

(x - 1)^{5} (x + 1) = (x - 1)^{5} x + (x - 1)^{5} \cdot 1

= (x - 1)^{5} x + (x - 1)^{5} \cdot 1

Vereinfache

(x - 1)^{5} x + (x - 1)^{5} \cdot 1 : x (x - 1)^{5} + (x - 1)^{5}

= x (x - 1)^{5} + (x - 1)^{5}

Schreibe

x (x - 1)^{5}

um:

x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x

= x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x + (x - 1)^{5}

Schreibe

(x - 1)^{5}

um:

(x)^{5} - 5 x^{2} + 10 (x)^{3} - 10 x + 5 x - 1

= x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x + (x)^{5} - 5 x^{2} + 10 (x)^{3} - 10 x + 5 x - 1

Vereinfache

x^{3} - 5 x^{2} x + 10 x^{2} - 10 x x + 5 x - x + (x)^{5} - 5 x^{2} + 10 (x)^{3} - 10 x + 5 x - 1 : x^{3} - 4 x^{2} x + 5 x^{2} - 5 x + 4 x - 1

= x^{3} - 4 x^{2} x + 5 x^{2} - 5 x + 4 x - 1

Beliebte Beispiele

erweitern x/((1-4x)^2)

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

erweitern ((2s^3-s^2))/((4s^2-4s+5)^2)

e x p an d \frac{( 2 s ^{3} - s ^{2} )}{( 4 s ^{2} - 4 s + 5 ) ^{2}}

erweitern (1-x/4)^{10}

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

erweitern (6-2x^{1/2})^2

e x p an d (6 - 2 x^{\frac{1}{2}})^{2}

erweitern 1/((s-1)(s^2+2s+2))

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