erweitern ((3z-1)^5)/(3(3z+2)^4)

Lösung

erweitern

\frac{( 3 z - 1 ) ^{5}}{3 ( 3 z + 2 ) ^{4}}

\frac{243 z ^{5} - 405 z ^{4} + 270 z ^{3} - 90 z ^{2} + 15 z - 1}{243 z ^{4} + 648 z ^{3} + 648 z ^{2} + 288 z + 48}

Schritte zur Lösung

\frac{( 3 z - 1 ) ^{5}}{3 ( 3 z + 2 ) ^{4}}

(3 z + 2)^{4} = 81 z^{4} + 216 z^{3} + 216 z^{2} + 96 z + 16

= \frac{( 3 z - 1 ) ^{5}}{3 ( 81 z ^{4} + 216 z ^{3} + 216 z ^{2} + 96 z + 16 )}

(3 z - 1)^{5} = 243 z^{5} - 405 z^{4} + 270 z^{3} - 90 z^{2} + 15 z - 1

= \frac{243 z ^{5} - 405 z ^{4} + 270 z ^{3} - 90 z ^{2} + 15 z - 1}{3 ( 81 z ^{4} + 216 z ^{3} + 216 z ^{2} + 96 z + 16 )}

Multipliziere aus

3 (81 z^{4} + 216 z^{3} + 216 z^{2} + 96 z + 16) : 243 z^{4} + 648 z^{3} + 648 z^{2} + 288 z + 48

= \frac{243 z ^{5} - 405 z ^{4} + 270 z ^{3} - 90 z ^{2} + 15 z - 1}{243 z ^{4} + 648 z ^{3} + 648 z ^{2} + 288 z + 48}

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

e x p an d (6 - 2 x) (\frac{7}{2} - 2 x) x

s im pl i f y 15 x + \frac{( 3 - 6 ) x ^{2}}{4}

e x p an d \frac{\partial}{\partial x} (5 e^{y}) + e^{y} (5 x + 5 y)

e x p an d \frac{3}{( v - 6 ) ( v + 2 )}