erweitern (2m^{1/2}-mn^{5/7})^3

Lösung

erweitern

(2 m^{\frac{1}{2}} - m n^{\frac{5}{7}})^{3}

8 m^{\frac{3}{2}} - 12 m^{2} n^{\frac{5}{7}} + 6 m^{\frac{5}{2}} n^{\frac{10}{7}} - m^{3} n^{\frac{15}{7}}

Schritte zur Lösung

(2 m^{\frac{1}{2}} - m n^{\frac{5}{7}})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(2 m^{\frac{1}{2}} - m n^{\frac{5}{7}})^{3} = (2 m^{\frac{1}{2}})^{3} - 3 (2 m^{\frac{1}{2}})^{2} m n^{\frac{5}{7}} + 3 \cdot 2 m^{\frac{1}{2}} (m n^{\frac{5}{7}})^{2} - (m n^{\frac{5}{7}})^{3}

= (2 m^{\frac{1}{2}})^{3} - 3 (2 m^{\frac{1}{2}})^{2} m n^{\frac{5}{7}} + 3 \cdot 2 m^{\frac{1}{2}} (m n^{\frac{5}{7}})^{2} - (m n^{\frac{5}{7}})^{3}

(2 m^{\frac{1}{2}})^{3} = 8 m^{\frac{3}{2}}

3 (2 m^{\frac{1}{2}})^{2} m n^{\frac{5}{7}} = 12 m^{2} n^{\frac{5}{7}}

3 \cdot 2 m^{\frac{1}{2}} (m n^{\frac{5}{7}})^{2} = 6 m^{\frac{5}{2}} n^{\frac{10}{7}}

(m n^{\frac{5}{7}})^{3} = m^{3} n^{\frac{15}{7}}

= 8 m^{\frac{3}{2}} - 12 m^{2} n^{\frac{5}{7}} + 6 m^{\frac{5}{2}} n^{\frac{10}{7}} - m^{3} n^{\frac{15}{7}}

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