erweitern-1/8 (x+2)^2(x-4)^2

Lösung

erweitern

- \frac{1}{8} (x + 2)^{2} (x - 4)^{2}

- \frac{x ^{4}}{8} + \frac{x ^{3}}{2} + \frac{3 x ^{2}}{2} - 4 x - 8

Schritte zur Lösung

- \frac{1}{8} (x + 2)^{2} (x - 4)^{2}

Schreibe

(x + 2)^{2}

um:

x^{2} + 4 x + 4

= - \frac{1}{8} (x^{2} + 4 x + 4) (x - 4)^{2}

= - \frac{1}{8} (x - 4)^{2} (x^{2} + 4 x + 4)

Schreibe

(x - 4)^{2}

um:

x^{2} - 8 x + 16

= - \frac{1}{8} (x^{2} - 8 x + 16) (x^{2} + 4 x + 4)

Schreibe

(x^{2} - 8 x + 16) (x^{2} + 4 x + 4)

um:

x^{4} - 4 x^{3} - 12 x^{2} + 32 x + 64

= - \frac{1}{8} (x^{4} - 4 x^{3} - 12 x^{2} + 32 x + 64)

Setze Klammern

= - \frac{1}{8} x^{4} - \frac{1}{8} (- 4 x^{3}) - \frac{1}{8} (- 12 x^{2}) - \frac{1}{8} \cdot 32 x - \frac{1}{8} \cdot 64

Vereinfache

- \frac{1}{8} x^{4} - \frac{1}{8} (- 4 x^{3}) - \frac{1}{8} (- 12 x^{2}) - \frac{1}{8} \cdot 32 x - \frac{1}{8} \cdot 64 : - \frac{x ^{4}}{8} + \frac{x ^{3}}{2} + \frac{3 x ^{2}}{2} - 4 x - 8

= - \frac{x ^{4}}{8} + \frac{x ^{3}}{2} + \frac{3 x ^{2}}{2} - 4 x - 8

s im pl i f y (1 - \frac{1}{x ^{2}}) \cdot (2 + x)

e x p an d f (12 x - 6) x^{2} d x

\frac{d}{d t} ((θ) (θ^{2} - t^{2})^{2})

\frac{\partial}{\partial x} ((z) (t x^{2} + yz - 2))

e x p an d x + 1 \cdot (x + 1)^{2}