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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

1^{3} = 1

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

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

(u^{\frac{1}{2}})^{3} = u^{\frac{3}{2}}

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

e x p an d cos^{2} (t) (1 - t) (7 - t^{3})

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