erweitern ((4x+1)^3)/(12)

Lösung

erweitern

\frac{( 4 x + 1 ) ^{3}}{12}

\frac{16 x ^{3}}{3} + 4 x^{2} + x + \frac{1}{12}

Schritte zur Lösung

\frac{( 4 x + 1 ) ^{3}}{12}

(4 x + 1)^{3} = 64 x^{3} + 48 x^{2} + 12 x + 1

= \frac{64 x ^{3} + 48 x ^{2} + 12 x + 1}{12}

Wende Bruchregel an:

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

\frac{64 x ^{3} + 48 x ^{2} + 12 x + 1}{12} = \frac{64 x ^{3}}{12} + \frac{48 x ^{2}}{12} + \frac{12 x}{12} + \frac{1}{12}

= \frac{64 x ^{3}}{12} + \frac{48 x ^{2}}{12} + \frac{12 x}{12} + \frac{1}{12}

Streiche

\frac{64 x ^{3}}{12} : \frac{16 x ^{3}}{3}

= \frac{16 x ^{3}}{3} + \frac{48 x ^{2}}{12} + \frac{12 x}{12} + \frac{1}{12}

Teile die Zahlen:

\frac{48}{12} = 4

= \frac{16 x ^{3}}{3} + 4 x^{2} + \frac{12 x}{12} + \frac{1}{12}

Teile die Zahlen:

\frac{12}{12} = 1

= \frac{16 x ^{3}}{3} + 4 x^{2} + x + \frac{1}{12}

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

e x p an d \frac{2 ( π ^{3} + 3 π ^{2} )}{3 π}