erweitern ((200-x)^6)/((80-x)^3)

Lösung

erweitern

\frac{( 200 - x ) ^{6}}{( 80 - x ) ^{3}}

\frac{20 0 ^{6} - 20 0 ^{5} \cdot 6 x + 20 0 ^{4} \cdot 15 x ^{2} - 160000000 x ^{3} + 600000 x ^{4} - 1200 x ^{5} + x ^{6}}{512000 - 19200 x + 240 x ^{2} - x ^{3}}

Schritte zur Lösung

\frac{( 200 - x ) ^{6}}{( 80 - x ) ^{3}}

(80 - x)^{3} = 512000 - 19200 x + 240 x^{2} - x^{3}

= \frac{( 200 - x ) ^{6}}{512000 - 19200 x + 240 x ^{2} - x ^{3}}

(200 - x)^{6} = 20 0^{6} - 20 0^{5} \cdot 6 x + 20 0^{4} \cdot 15 x^{2} - 160000000 x^{3} + 600000 x^{4} - 1200 x^{5} + x^{6}

= \frac{20 0 ^{6} - 20 0 ^{5} \cdot 6 x + 20 0 ^{4} \cdot 15 x ^{2} - 160000000 x ^{3} + 600000 x ^{4} - 1200 x ^{5} + x ^{6}}{512000 - 19200 x + 240 x ^{2} - x ^{3}}

e x p an d \frac{( 4 - 2 x ^{2} ) ^{2}}{16 - 3 x}

e x p an d (2 x - 2 x - 3)^{7}

e x p an d (4 e^{2 x} + 4 x e^{2 x}) (2 e^{2 x}) (x)

e x p an d \frac{1}{2 x ( 4 x - 50 )}

e x p an d e^{4 t} (t - 4)^{2}