erweitern (x+1/3)^3*(x+2/9)^2

Lösung

erweitern

(x + \frac{1}{3})^{3} \cdot (x + \frac{2}{9})^{2}

\frac{( 81 x ^{2} + 36 x + 4 ) ( 27 x ^{3} + 27 x ^{2} + 9 x + 1 )}{2187}

Schritte zur Lösung

(x + \frac{1}{3})^{3} (x + \frac{2}{9})^{2}

Schreibe

(x + \frac{2}{9})^{2}

um:

\frac{81 x ^{2} + 36 x + 4}{81}

= (x + \frac{1}{3})^{3} \frac{81 x ^{2} + 36 x + 4}{81}

= \frac{81 x ^{2} + 36 x + 4}{81} (x + \frac{1}{3})^{3}

Schreibe

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

um:

\frac{27 x ^{3} + 27 x ^{2} + 9 x + 1}{27}

= \frac{81 x ^{2} + 36 x + 4}{81} \cdot \frac{27 x ^{3} + 27 x ^{2} + 9 x + 1}{27}

Vereinfache

\frac{81 x ^{2} + 36 x + 4}{81} \cdot \frac{27 x ^{3} + 27 x ^{2} + 9 x + 1}{27} : \frac{( 81 x ^{2} + 36 x + 4 ) ( 27 x ^{3} + 27 x ^{2} + 9 x + 1 )}{2187}

= \frac{( 81 x ^{2} + 36 x + 4 ) ( 27 x ^{3} + 27 x ^{2} + 9 x + 1 )}{2187}

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

e x p an d \frac{727 ( - x + 3 )}{114}

e x p an d x \cdot (0.2 sin (0.3 t) + 0.6 cos (0.3 t))

e x p an d - \frac{6 ln ( 7 )}{35 ( 1 - e ^{\frac{l n ( 7 )}{35}} )}

s im pl i f y \frac{2197}{2000} (2 + lo g_{3} (2))