erweitern 2(x_{1}-x_{2}-x_{3})^2

Lösung

erweitern

2 (x_{1} - x_{2} - x_{3})^{2}

- 4 x_{1} x_{2} - 4 x_{1} x_{3} + 2 x_{1}^{2} + 2 x_{2}^{2} + 4 x_{2} x_{3} + 2 x_{3}^{2}

Schritte zur Lösung

2 (x_{1} - x_{2} - x_{3})^{2}

(x_{1} - x_{2} - x_{3})^{2} = - 2 x_{1} x_{2} - 2 x_{1} x_{3} + x_{1}^{2} + x_{2}^{2} + 2 x_{2} x_{3} + x_{3}^{2}

= 2 (x_{1}^{2} - 2 x_{1} x_{2} - 2 x_{1} x_{3} + x_{2}^{2} + 2 x_{2} x_{3} + x_{3}^{2})

Setze Klammern

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

Wende Minus-Plus Regeln an

+ (- a) = - a

= - 2 \cdot 2 x_{1} x_{2} - 2 \cdot 2 x_{1} x_{3} + 2 x_{1}^{2} + 2 x_{2}^{2} + 2 \cdot 2 x_{2} x_{3} + 2 x_{3}^{2}

Multipliziere die Zahlen:

2 \cdot 2 = 4

= - 4 x_{1} x_{2} - 4 x_{1} x_{3} + 2 x_{1}^{2} + 2 x_{2}^{2} + 4 x_{2} x_{3} + 2 x_{3}^{2}

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

e x p an d ((2 + cos (u) sin (u)))^{2}

e x p an d \frac{10 x + 9}{3 ( x + 1 ) ( 2 x + 3 )}

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

e x p an d \frac{4 x + 2}{( x - 2 ) ( 3 x + 4 )}