erweitern (12b^{20}-9m^{3/2})^2

Lösung

erweitern

(12 b^{20} - 9 m^{\frac{3}{2}})^{2}

144 b^{40} - 216 b^{20} m^{\frac{3}{2}} + 81 m^{3}

Schritte zur Lösung

(12 b^{20} - 9 m^{\frac{3}{2}})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(12 b^{20} - 9 m^{\frac{3}{2}})^{2} = (12 b^{20})^{2} - 2 \cdot 12 b^{20} \cdot 9 m^{\frac{3}{2}} + (9 m^{\frac{3}{2}})^{2}

= (12 b^{20})^{2} - 2 \cdot 12 b^{20} \cdot 9 m^{\frac{3}{2}} + (9 m^{\frac{3}{2}})^{2}

(12 b^{20})^{2} = 144 b^{40}

2 \cdot 12 b^{20} \cdot 9 m^{\frac{3}{2}} = 216 b^{20} m^{\frac{3}{2}}

(9 m^{\frac{3}{2}})^{2} = 81 m^{3}

= 144 b^{40} - 216 b^{20} m^{\frac{3}{2}} + 81 m^{3}

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