erweitern x^2(2-x)+1/3 (2-x)^3+(2-x)

Lösung

erweitern

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

4 x^{2} - \frac{4 x ^{3}}{3} + \frac{14}{3} - 5 x

Schritte zur Lösung

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

Apply rule:

a + (b + c) = a + b + c

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

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

Schreibe

x^{2} (2 - x)

um:

2 x^{2} - x^{3}

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

Schreibe

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

um:

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

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

Vereinfache

2 x^{2} - x^{3} + \frac{8}{3} - 4 x + 2 x^{2} - \frac{x ^{3}}{3} + 2 - x : 4 x^{2} - \frac{4 x ^{3}}{3} + \frac{14}{3} - 5 x

= 4 x^{2} - \frac{4 x ^{3}}{3} + \frac{14}{3} - 5 x

e x p an d t (- 9 cos (u) (a t) - 4 sin (a t))

s im pl i f y \frac{1}{4 \cdot π \cdot 0.02} (\frac{1}{0.75} - \frac{1}{0.85}) + \frac{1}{5}

e x p an d \frac{( 6 x ^{2} - 2 )}{( x ^{2} + 1 ) ^{3}}

s im pl i f y x - 3 (x + 3)

e x p an d \frac{1}{( x + 4 ) ( x ^{3} + 6 x ^{2} + 6 )}