erweitern (4x^2+2xy)^3

Lösung

erweitern

(4 x^{2} + 2 x y)^{3}

64 x^{6} + 96 x^{5} y + 48 x^{4} y^{2} + 8 x^{3} y^{3}

Schritte zur Lösung

(4 x^{2} + 2 x y)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(4 x^{2} + 2 x y)^{3} = (4 x^{2})^{3} + 3 (4 x^{2})^{2} \cdot 2 x y + 3 \cdot 4 x^{2} (2 x y)^{2} + (2 x y)^{3}

= (4 x^{2})^{3} + 3 (4 x^{2})^{2} \cdot 2 x y + 3 \cdot 4 x^{2} (2 x y)^{2} + (2 x y)^{3}

Vereinfache

(4 x^{2})^{3} + 3 (4 x^{2})^{2} \cdot 2 x y + 3 \cdot 4 x^{2} (2 x y)^{2} + (2 x y)^{3} : 64 x^{6} + 96 x^{5} y + 48 x^{4} y^{2} + 8 x^{3} y^{3}

= 64 x^{6} + 96 x^{5} y + 48 x^{4} y^{2} + 8 x^{3} y^{3}

e x p an d (a + b)^{2} - c^{2}

f a c t or m^{3} n^{2} p^{4} + m^{4} n^{3} p^{5} - m^{6} n^{4} p^{4} + m^{2} n^{4} p^{3}

e x p an d x (3 x^{2} + 2 x - 1)

f a c t or 20 x^{2} + 13 x + 2

s im pl i f y \frac{( \frac{2}{3} ) ^{3}}{( \frac{2}{3} ) ^{- 2}}