erweitern (a^3+b^3+c^3-27abc)/((a+b)(b+c)(a+c))

Lösung

erweitern

\frac{a ^{3} + b ^{3} + c ^{3} - 27 ab c}{( a + b ) ( b + c ) ( a + c )}

\frac{a ^{3} + b ^{3} + c ^{3} - 27 ab c}{a b ^{2} + a ^{2} b + 2 ab c + a ^{2} c + a c ^{2} + b ^{2} c + b c ^{2}}

Schritte zur Lösung

\frac{a ^{3} + b ^{3} + c ^{3} - 27 ab c}{( a + b ) ( b + c ) ( a + c )}

Multipliziere aus

(a + b) (b + c) (a + c) : a b^{2} + a^{2} b + 2 ab c + a^{2} c + a c^{2} + b^{2} c + b c^{2}

= \frac{a ^{3} + b ^{3} + c ^{3} - 27 ab c}{a b ^{2} + a ^{2} b + 2 ab c + a ^{2} c + a c ^{2} + b ^{2} c + b c ^{2}}

e x p an d, \frac{3}{2} (x - 2) - \frac{1}{2} (\frac{x}{3} - 1)

s im pl i f y e^{(a + 1) t} sin ((b + 2) x) sin^{2} ((c + 3) x)

e x p an d \frac{( 8 - x ) ^{5}}{40}

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

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