erweitern (ax+bx^{1/2}+c)^2

Lösung

erweitern

(a \cdot x + b \cdot x^{\frac{1}{2}} + c)^{2}

c^{2} + a^{2} x^{2} + 2 a x^{\frac{3}{2}} b + x b^{2} + 2 a c x + 2 x^{\frac{1}{2}} b c

Schritte zur Lösung

(a x + b x^{\frac{1}{2}} + c)^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(a x + b x^{\frac{1}{2}} + c)^{2} = (a x + b x^{\frac{1}{2}} + c) (a x + b x^{\frac{1}{2}} + c)

= (a x + b x^{\frac{1}{2}} + c) (a x + b x^{\frac{1}{2}} + c)

Setze Klammern

= a x a x + a x b x^{\frac{1}{2}} + a x c + b x^{\frac{1}{2}} a x + b x^{\frac{1}{2}} b x^{\frac{1}{2}} + b x^{\frac{1}{2}} c + c a x + c b x^{\frac{1}{2}} + cc

Vereinfache

a x a x + a x b x^{\frac{1}{2}} + a x c + b x^{\frac{1}{2}} a x + b x^{\frac{1}{2}} b x^{\frac{1}{2}} + b x^{\frac{1}{2}} c + c a x + c b x^{\frac{1}{2}} + cc : c^{2} + a^{2} x^{2} + 2 a x^{\frac{3}{2}} b + x b^{2} + 2 a c x + 2 x^{\frac{1}{2}} b c

= c^{2} + a^{2} x^{2} + 2 a x^{\frac{3}{2}} b + x b^{2} + 2 a c x + 2 x^{\frac{1}{2}} b c

e x p an d (sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

e x p an d - 6 (e^{x} - e^{2 x})

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

e x p an d \frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

s im pl i f y (\frac{3 x ^{3}}{2} + 9 y^{2}) (\frac{3 x ^{3}}{2} - 9 y^{2})