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

Lösung

erweitern

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

\frac{b ^{4}}{4} + b^{3} x + \frac{3 b ^{2} x ^{2}}{2} + b x^{3} + \frac{x ^{4}}{4}

Schritte zur Lösung

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

(b + x)^{4} = b^{4} + 4 b^{3} x + 6 b^{2} x^{2} + 4 b x^{3} + x^{4}

= \frac{b ^{4} + 4 b ^{3} x + 6 b ^{2} x ^{2} + 4 b x ^{3} + x ^{4}}{4}

Wende Bruchregel an:

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

\frac{b ^{4} + 4 b ^{3} x + 6 b ^{2} x ^{2} + 4 b x ^{3} + x ^{4}}{4} = \frac{b ^{4}}{4} + \frac{4 b ^{3} x}{4} + \frac{6 b ^{2} x ^{2}}{4} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

= \frac{b ^{4}}{4} + \frac{4 b ^{3} x}{4} + \frac{6 b ^{2} x ^{2}}{4} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

Teile die Zahlen:

\frac{4}{4} = 1

= \frac{b ^{4}}{4} + b^{3} x + \frac{6 b ^{2} x ^{2}}{4} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

Streiche

\frac{6 b ^{2} x ^{2}}{4} : \frac{3 b ^{2} x ^{2}}{2}

= \frac{b ^{4}}{4} + b^{3} x + \frac{3 b ^{2} x ^{2}}{2} + \frac{4 b x ^{3}}{4} + \frac{x ^{4}}{4}

Teile die Zahlen:

\frac{4}{4} = 1

= \frac{b ^{4}}{4} + b^{3} x + \frac{3 b ^{2} x ^{2}}{2} + b x^{3} + \frac{x ^{4}}{4}

e x p an d (x + 1)^{5} e^{3 x^{2}}

e x p an d, (5 a^{2} - 2 b + c^{3}) (3 x - 2 y - 5 z + 2)

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

e x p an d 4^{\frac{3}{2}}

e x p an d A (- 4, 2) B (6, 4) C (8, - 5)