vereinfachen (xsqrt(y^2+1)+ysqrt(x^2+1))^2

Lösung

vereinfachen

(x y^{2} + 1 + y x^{2} + 1)^{2}

2 x^{2} y^{2} + x^{2} + 2 x y y^{2} + 1 x^{2} + 1 + y^{2}

Schritte zur Lösung

(x y^{2} + 1 + y x^{2} + 1)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(x y^{2} + 1 + y x^{2} + 1)^{2} = (x y^{2} + 1)^{2} + 2 x y^{2} + 1 y x^{2} + 1 + (y x^{2} + 1)^{2}

= (x y^{2} + 1)^{2} + 2 x y^{2} + 1 y x^{2} + 1 + (y x^{2} + 1)^{2}

(x y^{2} + 1)^{2} = x^{2} (y^{2} + 1)

2 x y^{2} + 1 y x^{2} + 1 = 2 x y y^{2} + 1 x^{2} + 1

(y x^{2} + 1)^{2} = y^{2} (x^{2} + 1)

= x^{2} (y^{2} + 1) + 2 x y y^{2} + 1 x^{2} + 1 + y^{2} (x^{2} + 1)

Vereinfache

x^{2} (y^{2} + 1) + 2 x y y^{2} + 1 x^{2} + 1 + y^{2} (x^{2} + 1) : 2 x^{2} y^{2} + x^{2} + 2 x y y^{2} + 1 x^{2} + 1 + y^{2}

= 2 x^{2} y^{2} + x^{2} + 2 x y y^{2} + 1 x^{2} + 1 + y^{2}

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

e x p an d cot (x) \cdot (sec (x) + tan (x))

s im pl i f y (4 - i)^{6}

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

e x p an d \frac{4 π}{( w - π ) ^{2}}