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

Lösung

erweitern

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

6 x^{2} y^{2} + 3 x^{4} - 6 x^{2} + 3 y^{4} - 6 y^{2} + 3

Schritte zur Lösung

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

(x^{2} + y^{2} - 1)^{2} = 2 x^{2} y^{2} + x^{4} - 2 x^{2} + y^{4} - 2 y^{2} + 1

= 3 (x^{4} + 2 x^{2} y^{2} - 2 x^{2} + y^{4} + 1 - 2 y^{2})

Setze Klammern

= 3 \cdot 2 x^{2} y^{2} + 3 x^{4} + 3 (- 2 x^{2}) + 3 y^{4} + 3 (- 2 y^{2}) + 3 \cdot 1

Wende Minus-Plus Regeln an

+ (- a) = - a

= 3 \cdot 2 x^{2} y^{2} + 3 x^{4} - 3 \cdot 2 x^{2} + 3 y^{4} - 3 \cdot 2 y^{2} + 3 \cdot 1

Vereinfache

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

= 6 x^{2} y^{2} + 3 x^{4} - 6 x^{2} + 3 y^{4} - 6 y^{2} + 3

e x p an d (x^{2} - 3) \cdot e^{x}

e x p an d (\frac{x}{3} + \frac{y}{2} = 7) 3

e x p an d \frac{6}{( 5 x - 4 ) ^{2}}

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

e x p an d \frac{x ( x + 3 )}{2 ( x + 2 )}