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

Lösung

erweitern

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

x^{\frac{3}{2}} - 2 x^{\frac{5}{2}} + x^{\frac{7}{2}}

Schritte zur Lösung

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

Schreibe

(1 - x)^{2}

um:

1 - 2 x + x^{2}

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

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

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

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

x^{\frac{3}{2}} \cdot 1 = x^{\frac{3}{2}}

x^{\frac{3}{2}} (- 2 x) = - 2 x^{\frac{5}{2}}

x^{\frac{3}{2}} x^{2} = x^{\frac{7}{2}}

= x^{\frac{3}{2}} - 2 x^{\frac{5}{2}} + x^{\frac{7}{2}}

s im pl i f y - 16 (3 x^{2} sin (x^{4}) + 4 x^{6} cos (x^{4}))

s im pl i f y (1 - x - 1)^{2}

e x p an d \frac{in d i c a d a}{( x + y + 3 ) ^{2}}

e x p an d - \frac{( 6 - x ) ( - 6 + x )}{9}

e x p an d e^{4 x} (e^{2 x} + 3)