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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

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

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

Apply rule:

a \cdot 1 = a

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

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

s im pl i f y - 2 (3 - 52)

e x p an d \frac{12}{s ( s + 10 ) ( s + 70 )}

s im pl i f y (\frac{x}{3} - 2) (\frac{x}{3} - 3)

s im pl i f y (x + 3) (x - 3) (x - 2)

e x p an d 7 (\frac{3}{5} u - \frac{3}{23} v)^{2}