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

Lösung

erweitern

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

x^{2} + 6 x - 2 e^{\frac{2 x}{3}} x - 6 e^{\frac{2 x}{3}} + e^{\frac{4 x}{3}} + 9

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

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

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

Multipliziere aus

(x + 3 - e^{\frac{2 x}{3}}) (x + 3 - e^{\frac{2 x}{3}}) : x^{2} + 6 x - 2 e^{\frac{2 x}{3}} x - 6 e^{\frac{2 x}{3}} + e^{\frac{4 x}{3}} + 9

= x^{2} + 6 x - 2 e^{\frac{2 x}{3}} x - 6 e^{\frac{2 x}{3}} + e^{\frac{4 x}{3}} + 9

e x p an d 2 (e^{x} + 1) e^{x}

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

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

e x p an d \frac{x ^{3} + 48 x ^{2} + 65 x - 240}{( x - 8 ) ( x ^{2} + 5 )}

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