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

Lösung

erweitern

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

(x + 1)^{\frac{2}{3}} \cdot 27 x^{6} - 54 x^{4} (x + 1)^{\frac{2}{3}} + (x + 1)^{\frac{2}{3}} \cdot 36 x^{2} - 8 (x + 1)^{\frac{2}{3}}

Schritte zur Lösung

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

Schreibe

(3 x^{2} - 2)^{3}

um:

27 x^{6} - 54 x^{4} + 36 x^{2} - 8

= (x + 1)^{\frac{2}{3}} (27 x^{6} - 54 x^{4} + 36 x^{2} - 8)

Setze Klammern

= (x + 1)^{\frac{2}{3}} \cdot 27 x^{6} + (x + 1)^{\frac{2}{3}} (- 54 x^{4}) + (x + 1)^{\frac{2}{3}} \cdot 36 x^{2} + (x + 1)^{\frac{2}{3}} (- 8)

(x + 1)^{\frac{2}{3}} (- 54 x^{4}) = - 54 x^{4} (x + 1)^{\frac{2}{3}}

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

= (x + 1)^{\frac{2}{3}} \cdot 27 x^{6} - 54 x^{4} (x + 1)^{\frac{2}{3}} + (x + 1)^{\frac{2}{3}} \cdot 36 x^{2} - 8 (x + 1)^{\frac{2}{3}}

e x p an d \frac{3 x ^{2}}{ln ( 10 ) ( x ^{3} + 1 )}

e x p an d \frac{1}{12} (sin (x^{2}) + cos (x^{2})) (4 + sin (2) x^{2})

e x p an d \frac{x ^{n}}{x ^{8}}

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

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