erweitern-3(8x^2-8x+1)(2x-1)^3(x^2-x)^{1/2}

Lösung

erweitern

- 3 (8 x^{2} - 8 x + 1) (2 x - 1)^{3} (x^{2} - x)^{\frac{1}{2}}

- 192 x^{5} (x^{2} - x)^{\frac{1}{2}} + 480 x^{4} (x^{2} - x)^{\frac{1}{2}} - 456 x^{3} (x^{2} - x)^{\frac{1}{2}} + 204 x^{2} (x^{2} - x)^{\frac{1}{2}} - 42 x (x^{2} - x)^{\frac{1}{2}} + 3 (x^{2} - x)^{\frac{1}{2}}

Schritte zur Lösung

- 3 (8 x^{2} - 8 x + 1) (2 x - 1)^{3} (x^{2} - x)^{\frac{1}{2}}

= - 3 (2 x - 1)^{3} (x^{2} - x)^{\frac{1}{2}} (8 x^{2} - 8 x + 1)

Schreibe

(2 x - 1)^{3}

um:

8 x^{3} - 12 x^{2} + 6 x - 1

= - 3 (8 x^{3} - 12 x^{2} + 6 x - 1) (x^{2} - x)^{\frac{1}{2}} (8 x^{2} - 8 x + 1)

= - 3 (x^{2} - x)^{\frac{1}{2}} (8 x^{3} - 12 x^{2} + 6 x - 1) (8 x^{2} - 8 x + 1)

Schreibe

(8 x^{3} - 12 x^{2} + 6 x - 1) (8 x^{2} - 8 x + 1)

um:

64 x^{5} - 160 x^{4} + 152 x^{3} - 68 x^{2} + 14 x - 1

= - 3 (x^{2} - x)^{\frac{1}{2}} (64 x^{5} - 160 x^{4} + 152 x^{3} - 68 x^{2} + 14 x - 1)

Setze Klammern

= - 3 (x^{2} - x)^{\frac{1}{2}} \cdot 64 x^{5} - 3 (x^{2} - x)^{\frac{1}{2}} (- 160 x^{4}) - 3 (x^{2} - x)^{\frac{1}{2}} \cdot 152 x^{3} - 3 (x^{2} - x)^{\frac{1}{2}} (- 68 x^{2}) - 3 (x^{2} - x)^{\frac{1}{2}} \cdot 14 x - 3 (x^{2} - x)^{\frac{1}{2}} (- 1)

Vereinfache

- 3 (x^{2} - x)^{\frac{1}{2}} \cdot 64 x^{5} - 3 (x^{2} - x)^{\frac{1}{2}} (- 160 x^{4}) - 3 (x^{2} - x)^{\frac{1}{2}} \cdot 152 x^{3} - 3 (x^{2} - x)^{\frac{1}{2}} (- 68 x^{2}) - 3 (x^{2} - x)^{\frac{1}{2}} \cdot 14 x - 3 (x^{2} - x)^{\frac{1}{2}} (- 1) : - 192 x^{5} (x^{2} - x)^{\frac{1}{2}} + 480 x^{4} (x^{2} - x)^{\frac{1}{2}} - 456 x^{3} (x^{2} - x)^{\frac{1}{2}} + 204 x^{2} (x^{2} - x)^{\frac{1}{2}} - 42 x (x^{2} - x)^{\frac{1}{2}} + 3 (x^{2} - x)^{\frac{1}{2}}

= - 192 x^{5} (x^{2} - x)^{\frac{1}{2}} + 480 x^{4} (x^{2} - x)^{\frac{1}{2}} - 456 x^{3} (x^{2} - x)^{\frac{1}{2}} + 204 x^{2} (x^{2} - x)^{\frac{1}{2}} - 42 x (x^{2} - x)^{\frac{1}{2}} + 3 (x^{2} - x)^{\frac{1}{2}}

s im pl i f y - 2 x (2 x + 5 y)

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

\frac{d}{d t} ((x) (x - y + z + t - 1))

e x p an d \frac{( 1 - 2 s )}{( s ^{2} + 4 s + 5 )}

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