erweitern (8x^{3/4}-2x^5)^2

Lösung

erweitern

(8 x^{\frac{3}{4}} - 2 x^{5})^{2}

64 x^{\frac{3}{2}} - 32 x^{\frac{23}{4}} + 4 x^{10}

Schritte zur Lösung

(8 x^{\frac{3}{4}} - 2 x^{5})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(8 x^{\frac{3}{4}} - 2 x^{5})^{2} = (8 x^{\frac{3}{4}})^{2} - 2 \cdot 8 x^{\frac{3}{4}} \cdot 2 x^{5} + (2 x^{5})^{2}

= (8 x^{\frac{3}{4}})^{2} - 2 \cdot 8 x^{\frac{3}{4}} \cdot 2 x^{5} + (2 x^{5})^{2}

(8 x^{\frac{3}{4}})^{2} = 64 x^{\frac{3}{2}}

2 \cdot 8 x^{\frac{3}{4}} \cdot 2 x^{5} = 32 x^{\frac{23}{4}}

(2 x^{5})^{2} = 4 x^{10}

= 64 x^{\frac{3}{2}} - 32 x^{\frac{23}{4}} + 4 x^{10}

e x p an d \frac{e ^{- s}}{s ( s - 3 ) ( s - 2 )}

e x p an d \frac{3 e ^{- s} - 3 s ^{- 2 s}}{s ( s ^{2} - 1 )}

e x p an d (3 sin (x) + cos (x))^{2}

e x p an d (tan (4 x) - tan (x)) \cdot (cos (5 x) + cos (3 x))

e x p an d \frac{2 x ( x ^{2} - 12 )}{( x ^{2} + 4 ) ^{3}}