erweitern (x^2+y^2+1)^2

Lösung

erweitern

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

x^{4} + y^{4} + x^{2} y^{2} + 2 x^{2} + y^{2} x^{2} + 2 y^{2} + 1

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Setze Klammern

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

Vereinfache

x^{2} x^{2} + x^{2} y^{2} + x^{2} \cdot 1 + y^{2} x^{2} + y^{2} y^{2} + y^{2} \cdot 1 + 1 \cdot x^{2} + 1 \cdot y^{2} + 1 \cdot 1 : x^{4} + y^{4} + x^{2} y^{2} + 2 x^{2} + y^{2} x^{2} + 2 y^{2} + 1

= x^{4} + y^{4} + x^{2} y^{2} + 2 x^{2} + y^{2} x^{2} + 2 y^{2} + 1

e x p an d (x - 8) (x - 1)

s im pl i f y 1 + 3.3 lo g_{10} (25)

s im pl i f y \frac{sin ^{2} ( x )}{tan ^{2} ( x )}

s im pl i f y g^{2} h 5 g

f a c t or x^{32} - 1