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

Lösung

erweitern

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

x^{3} + 2 x^{\frac{3}{2}} + 1

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

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

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

1^{2} = 1

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

e x p an d \frac{x ^{4} + 3 x ^{2}}{( x ^{2} + 1 ) ^{2}}

e x p an d sin (x) cos (x) (sec (x) + cot (x))

s im pl i f y x (1 - \frac{4}{x + 3})

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