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

Lösung

erweitern

\frac{- 1}{4} (x + 2)^{2} (x - 1)^{2}

- \frac{x ^{4}}{4} - \frac{x ^{3}}{2} + \frac{3 x ^{2}}{4} + x - 1

Schritte zur Lösung

\frac{- 1}{4} (x + 2)^{2} (x - 1)^{2}

Schreibe

(x + 2)^{2}

um:

x^{2} + 4 x + 4

= \frac{- 1}{4} (x^{2} + 4 x + 4) (x - 1)^{2}

= \frac{- 1}{4} (x - 1)^{2} (x^{2} + 4 x + 4)

Schreibe

(x - 1)^{2}

um:

x^{2} - 2 x + 1

= \frac{- 1}{4} (x^{2} - 2 x + 1) (x^{2} + 4 x + 4)

Schreibe

(x^{2} - 2 x + 1) (x^{2} + 4 x + 4)

um:

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

= \frac{- 1}{4} (x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4)

Setze Klammern

= \frac{- 1}{4} x^{4} + \frac{- 1}{4} \cdot 2 x^{3} + \frac{- 1}{4} (- 3 x^{2}) + \frac{- 1}{4} (- 4 x) + \frac{- 1}{4} \cdot 4

Vereinfache

\frac{- 1}{4} x^{4} + \frac{- 1}{4} \cdot 2 x^{3} + \frac{- 1}{4} (- 3 x^{2}) + \frac{- 1}{4} (- 4 x) + \frac{- 1}{4} \cdot 4 : - \frac{x ^{4}}{4} - \frac{x ^{3}}{2} + \frac{3 x ^{2}}{4} + x - 1

= - \frac{x ^{4}}{4} - \frac{x ^{3}}{2} + \frac{3 x ^{2}}{4} + x - 1

e x p an d (y + 1) (y + 4 - 4 y + 1)

e x p an d (e^{x} cos (2 x)) (e^{x} sin (2 x) + 2 e^{x} cos (2 x))

e x p an d (m + p = 5, 5) (f (p) - p = 2, 7) (f (p) + m = 28)

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

s im pl i f y (4 + 6 i)^{8}