erweitern (3x^2+2y^2-1)^2

Lösung

erweitern

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

9 x^{4} + 4 y^{4} + 6 x^{2} y^{2} - 6 x^{2} + 6 y^{2} x^{2} - 4 y^{2} + 1

Schritte zur Lösung

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

Wende Exponentenregel an:

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

(3 x^{2} + 2 y^{2} - 1)^{2} = (3 x^{2} + 2 y^{2} - 1) (3 x^{2} + 2 y^{2} - 1)

= (3 x^{2} + 2 y^{2} - 1) (3 x^{2} + 2 y^{2} - 1)

Setze Klammern

= 3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 y^{2} + 3 x^{2} (- 1) + 2 y^{2} \cdot 3 x^{2} + 2 y^{2} \cdot 2 y^{2} + 2 y^{2} (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 2 y^{2} - 1 \cdot (- 1)

Vereinfache

3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 y^{2} + 3 x^{2} (- 1) + 2 y^{2} \cdot 3 x^{2} + 2 y^{2} \cdot 2 y^{2} + 2 y^{2} (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 2 y^{2} - 1 \cdot (- 1) : 9 x^{4} + 4 y^{4} + 6 x^{2} y^{2} - 6 x^{2} + 6 y^{2} x^{2} - 4 y^{2} + 1

= 9 x^{4} + 4 y^{4} + 6 x^{2} y^{2} - 6 x^{2} + 6 y^{2} x^{2} - 4 y^{2} + 1

f a c t or 2 a^{2} + 5 ab + 2 b^{2}

f a c t or 121 - x^{4}

s im pl i f y - 49 x^{2}

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

f a c t or b^{4} - 64