erweitern (3a(a-2b)^2)/(2b^3)

Lösung

erweitern

\frac{3 a ( a - 2 b ) ^{2}}{2 b ^{3}}

\frac{3 a ^{3}}{2 b ^{3}} - \frac{6 a ^{2}}{b ^{2}} + \frac{6 a}{b}

Schritte zur Lösung

\frac{3 a ( a - 2 b ) ^{2}}{2 b ^{3}}

(a - 2 b)^{2} = a^{2} - 4 ab + 4 b^{2}

= \frac{3 a ( a ^{2} - 4 ab + 4 b ^{2} )}{2 b ^{3}}

Multipliziere aus

3 a (a^{2} - 4 ab + 4 b^{2}) : 3 a^{3} - 12 a^{2} b + 12 a b^{2}

= \frac{3 a ^{3} - 12 a ^{2} b + 12 a b ^{2}}{2 b ^{3}}

Wende Bruchregel an:

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

\frac{3 a ^{3} - 12 a ^{2} b + 12 a b ^{2}}{2 b ^{3}} = \frac{3 a ^{3}}{2 b ^{3}} - \frac{12 a ^{2} b}{2 b ^{3}} + \frac{12 a b ^{2}}{2 b ^{3}}

= \frac{3 a ^{3}}{2 b ^{3}} - \frac{12 a ^{2} b}{2 b ^{3}} + \frac{12 a b ^{2}}{2 b ^{3}}

Streiche

\frac{12 a ^{2} b}{2 b ^{3}} : \frac{6 a ^{2}}{b ^{2}}

= \frac{3 a ^{3}}{2 b ^{3}} - \frac{6 a ^{2}}{b ^{2}} + \frac{12 a b ^{2}}{2 b ^{3}}

Streiche

\frac{12 a b ^{2}}{2 b ^{3}} : \frac{6 a}{b}

= \frac{3 a ^{3}}{2 b ^{3}} - \frac{6 a ^{2}}{b ^{2}} + \frac{6 a}{b}

e x p an d α (c α, a α + b α + c α, 4 a α + 2 b α + c α)

e x p an d - \frac{8 s + 25}{( s + 4 ) ^{2}}

e x p an d (1 + j) e^{\frac{jπ t}{2}}

e x p an d (p + t) (e + t)

e x p an d \frac{100 ( s + 25 )}{s ( s + 5 ) ^{3}}