erweitern (1/4 x^2-1/(x^2))^2

Lösung

erweitern

(\frac{1}{4} x^{2} - \frac{1}{x ^{2}})^{2}

\frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

Schritte zur Lösung

(\frac{1}{4} x^{2} - \frac{1}{x ^{2}})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(\frac{1}{4} x^{2} - \frac{1}{x ^{2}})^{2} = (\frac{1}{4} x^{2})^{2} - 2 \cdot \frac{1}{4} x^{2} \frac{1}{x ^{2}} + (\frac{1}{x ^{2}})^{2}

= (\frac{1}{4} x^{2})^{2} - 2 \cdot \frac{1}{4} x^{2} \frac{1}{x ^{2}} + (\frac{1}{x ^{2}})^{2}

Vereinfache

(\frac{1}{4} x^{2})^{2} - 2 \cdot \frac{1}{4} x^{2} \frac{1}{x ^{2}} + (\frac{1}{x ^{2}})^{2} : \frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

= \frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

e x p an d \frac{A}{S + 1} \cdot (S + 1) (S - 1) (S + 2) (S^{2} + 1)

e x p an d (7 - 5 \frac{x}{96889010407})^{20}

s im pl i f y (10 - y) (\frac{y}{3} + 8)

e x p an d 7 x^{\frac{7}{5}} (x^{\frac{11}{5}} - 2 x)

s im pl i f y (3 a + 9) (3 a + 4)