erweitern ((11x^4+2)^5)/2

Lösung

erweitern

\frac{( 11 x ^{4} + 2 ) ^{5}}{2}

\frac{161051 x ^{20}}{2} + 73205 x^{16} + 26620 x^{12} + 4840 x^{8} + 440 x^{4} + 16

Schritte zur Lösung

\frac{( 11 x ^{4} + 2 ) ^{5}}{2}

(11 x^{4} + 2)^{5} = 161051 x^{20} + 146410 x^{16} + 53240 x^{12} + 9680 x^{8} + 880 x^{4} + 32

= \frac{161051 x ^{20} + 146410 x ^{16} + 53240 x ^{12} + 9680 x ^{8} + 880 x ^{4} + 32}{2}

Wende Bruchregel an:

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

\frac{161051 x ^{20} + 146410 x ^{16} + 53240 x ^{12} + 9680 x ^{8} + 880 x ^{4} + 32}{2} = \frac{161051 x ^{20}}{2} + \frac{146410 x ^{16}}{2} + \frac{53240 x ^{12}}{2} + \frac{9680 x ^{8}}{2} + \frac{880 x ^{4}}{2} + \frac{32}{2}

= \frac{161051 x ^{20}}{2} + \frac{146410 x ^{16}}{2} + \frac{53240 x ^{12}}{2} + \frac{9680 x ^{8}}{2} + \frac{880 x ^{4}}{2} + \frac{32}{2}

\frac{146410 x ^{16}}{2} = 73205 x^{16}

\frac{53240 x ^{12}}{2} = 26620 x^{12}

\frac{9680 x ^{8}}{2} = 4840 x^{8}

\frac{880 x ^{4}}{2} = 440 x^{4}

\frac{32}{2} = 16

= \frac{161051 x ^{20}}{2} + 73205 x^{16} + 26620 x^{12} + 4840 x^{8} + 440 x^{4} + 16

e x p an d (x_{0} + e x_{1} + x_{2} e^{2})^{3}

\frac{d}{d x} ((z) (2 x^{2} + 3 y^{2} + 5 z^{2} - 9))

e x p an d e^{z} (z + 1)

e x p an d \frac{x - 8}{( x + 2 ) ( x ^{2} - 4 )}

e x p an d ln (x) (x ln (x) - x)