erweitern (2x(-2x+6)^3)/(81)

Lösung

erweitern

\frac{2 x ( - 2 x + 6 ) ^{3}}{81}

- \frac{16 x ^{4}}{81} + \frac{16 x ^{3}}{9} - \frac{16 x ^{2}}{3} + \frac{16 x}{3}

Schritte zur Lösung

\frac{2 x ( - 2 x + 6 ) ^{3}}{81}

(- 2 x + 6)^{3} = - 8 x^{3} + 72 x^{2} - 216 x + 216

= \frac{2 x ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{81}

Multipliziere aus

2 x (- 8 x^{3} + 72 x^{2} - 216 x + 216) : - 16 x^{4} + 144 x^{3} - 432 x^{2} + 432 x

= \frac{- 16 x ^{4} + 144 x ^{3} - 432 x ^{2} + 432 x}{81}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 16 x ^{4} + 144 x ^{3} - 432 x ^{2} + 432 x}{81} = - \frac{16 x ^{4}}{81} + \frac{144 x ^{3}}{81} - \frac{432 x ^{2}}{81} + \frac{432 x}{81}

= - \frac{16 x ^{4}}{81} + \frac{144 x ^{3}}{81} - \frac{432 x ^{2}}{81} + \frac{432 x}{81}

Streiche

\frac{144 x ^{3}}{81} : \frac{16 x ^{3}}{9}

= - \frac{16 x ^{4}}{81} + \frac{16 x ^{3}}{9} - \frac{432 x ^{2}}{81} + \frac{432 x}{81}

Streiche

\frac{432 x ^{2}}{81} : \frac{16 x ^{2}}{3}

= - \frac{16 x ^{4}}{81} + \frac{16 x ^{3}}{9} - \frac{16 x ^{2}}{3} + \frac{432 x}{81}

Streiche

\frac{432 x}{81} : \frac{16 x}{3}

= - \frac{16 x ^{4}}{81} + \frac{16 x ^{3}}{9} - \frac{16 x ^{2}}{3} + \frac{16 x}{3}

\frac{\partial}{\partial x} ((f (x, y)) (x y - y^{2}))

e x p an d \frac{2 π}{365} (x - 114)

e x p an d \frac{( 8 - x ^{2} - y ^{2} ) ^{3}}{3}

e x p an d \frac{( s + 2 )}{( s + 3 ) \cdot ( s + 6 ) \cdot ( s + 8 )}

s im pl i f y 1 0^{10} δ (x - 9)