erweitern ((a-b)^2x^3)/(102)

Lösung

erweitern

\frac{( a - b ) ^{2} x ^{3}}{102}

\frac{a ^{2} x ^{3}}{102} - \frac{ab x ^{3}}{51} + \frac{b ^{2} x ^{3}}{102}

Schritte zur Lösung

\frac{( a - b ) ^{2} x ^{3}}{102}

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

= \frac{x ^{3} ( a ^{2} - 2 ab + b ^{2} )}{102}

Multipliziere aus

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

= \frac{a ^{2} x ^{3} - 2 ab x ^{3} + b ^{2} x ^{3}}{102}

Wende Bruchregel an:

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

\frac{a ^{2} x ^{3} - 2 ab x ^{3} + b ^{2} x ^{3}}{102} = \frac{a ^{2} x ^{3}}{102} - \frac{2 ab x ^{3}}{102} + \frac{b ^{2} x ^{3}}{102}

= \frac{a ^{2} x ^{3}}{102} - \frac{2 ab x ^{3}}{102} + \frac{b ^{2} x ^{3}}{102}

Streiche

\frac{2 ab x ^{3}}{102} : \frac{ab x ^{3}}{51}

= \frac{a ^{2} x ^{3}}{102} - \frac{ab x ^{3}}{51} + \frac{b ^{2} x ^{3}}{102}

e x p an d \frac{x - 5}{( x - 1 ) ^{3}}

f (x) = \frac{( 4 x - 3 ) ^{3}}{( 2 x - 3 ) ^{4}}

e x p an d \frac{1}{5} (5 x ln (5 x - e) - 10 x - e ln (5 x - e) + 2 e = 44.8)

e x p an d sin ((x + h)^{2})

e x p an d (x - 7)^{6}