faktorisieren x^4+x^2y^2+y^4

Lösung

faktorisieren

x^{4} + x^{2} y^{2} + y^{4}

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

Schritte zur Lösung

x^{4} + x^{2} y^{2} + y^{4}

Addiere und subtrahiere

x^{2} y^{2}

= x^{4} + 2 x^{2} y^{2} + y^{4} - x^{2} y^{2}

Faktorisiere

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

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

Wende Exponentenregel an:

a^{m} b^{m} = (ab)^{m}

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

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

Faktorisiere

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

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

s im pl i f y \frac{\frac{15}{x ^{2}}}{\frac{10}{x ^{5}}}

s im pl i f y (2 x - 3 y + 4 z) + (5 x + y - 3 z)

s im pl i f y ln (e^{e^{2}})

s im pl i f y \frac{3}{5} x + 19 - \frac{3}{20} x - 7

e x p an d (y - 5)^{3}