erweitern ((x+6)^4)/4

Lösung

erweitern

\frac{( x + 6 ) ^{4}}{4}

\frac{x ^{4}}{4} + 6 x^{3} + 54 x^{2} + 216 x + 324

Schritte zur Lösung

\frac{( x + 6 ) ^{4}}{4}

(x + 6)^{4} = x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296

= \frac{x ^{4} + 24 x ^{3} + 216 x ^{2} + 864 x + 1296}{4}

Wende Bruchregel an:

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

\frac{x ^{4} + 24 x ^{3} + 216 x ^{2} + 864 x + 1296}{4} = \frac{x ^{4}}{4} + \frac{24 x ^{3}}{4} + \frac{216 x ^{2}}{4} + \frac{864 x}{4} + \frac{1296}{4}

= \frac{x ^{4}}{4} + \frac{24 x ^{3}}{4} + \frac{216 x ^{2}}{4} + \frac{864 x}{4} + \frac{1296}{4}

\frac{24 x ^{3}}{4} = 6 x^{3}

\frac{216 x ^{2}}{4} = 54 x^{2}

\frac{864 x}{4} = 216 x

\frac{1296}{4} = 324

= \frac{x ^{4}}{4} + 6 x^{3} + 54 x^{2} + 216 x + 324

e x p an d (x + 2) (\cdot + 5)

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

e x p an d \frac{4 x ^{2} ( 30 - 2 x )}{9}

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

e x p an d \frac{( 2 x + 3 )}{( x - 5 ) ( x + 4 )}