vereinfachen (2a-sqrt((x-c)^2+y^2))^2

Lösung

vereinfachen

(2 a - (x - c)^{2} + y^{2})^{2}

4 a^{2} - 4 a (x - c)^{2} + y^{2} + (x - c)^{2} + y^{2}

Schritte zur Lösung

(2 a - (x - c)^{2} + y^{2})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(2 a - (x - c)^{2} + y^{2})^{2} = (2 a)^{2} - 2 \cdot 2 a (x - c)^{2} + y^{2} + ((x - c)^{2} + y^{2})^{2}

= (2 a)^{2} - 2 \cdot 2 a (x - c)^{2} + y^{2} + ((x - c)^{2} + y^{2})^{2}

(2 a)^{2} = 4 a^{2}

- 2 \cdot 2 a (x - c)^{2} + y^{2} = - 4 a (x - c)^{2} + y^{2}

((x - c)^{2} + y^{2})^{2} = (x - c)^{2} + y^{2}

= 4 a^{2} - 4 a (x - c)^{2} + y^{2} + (x - c)^{2} + y^{2}

e x p an d \frac{( 1 - sin ( x ) + t ^{2} ) t}{( 1 + t ^{2} ) ^{2}}

e x p an d (2 cos (x) - 1) (2 cos (x) + 1)

e x p an d 4 (x + h) - 3 - 4 x - 3

e x p an d x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

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