erweitern ((2x-b+g)(2x-a+b))/4

Lösung

erweitern

\frac{( 2 x - b + g ) ( 2 x - a + b )}{4}

x^{2} - \frac{a x}{2} + \frac{ba}{4} - \frac{b ^{2}}{4} + \frac{xg}{2} - \frac{a g}{4} + \frac{b g}{4}

Schritte zur Lösung

\frac{( 2 x - b + g ) ( 2 x - a + b )}{4}

Multipliziere aus

(2 x - b + g) (2 x - a + b) : 4 x^{2} - 2 a x + ba - b^{2} + 2 xg - a g + b g

= \frac{4 x ^{2} - 2 a x + ba - b ^{2} + 2 xg - a g + b g}{4}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{4 x ^{2} - 2 a x + ba - b ^{2} + 2 xg - a g + b g}{4} = \frac{4 x ^{2}}{4} - \frac{2 a x}{4} + \frac{ba}{4} - \frac{b ^{2}}{4} + \frac{2 xg}{4} - \frac{a g}{4} + \frac{b g}{4}

= \frac{4 x ^{2}}{4} - \frac{2 a x}{4} + \frac{ba}{4} - \frac{b ^{2}}{4} + \frac{2 xg}{4} - \frac{a g}{4} + \frac{b g}{4}

Teile die Zahlen:

\frac{4}{4} = 1

= x^{2} - \frac{2 a x}{4} + \frac{ba}{4} - \frac{b ^{2}}{4} + \frac{2 xg}{4} - \frac{a g}{4} + \frac{b g}{4}

Streiche

\frac{2 a x}{4} : \frac{a x}{2}

= x^{2} - \frac{a x}{2} + \frac{ba}{4} - \frac{b ^{2}}{4} + \frac{2 xg}{4} - \frac{a g}{4} + \frac{b g}{4}

Streiche

\frac{2 xg}{4} : \frac{xg}{2}

= x^{2} - \frac{a x}{2} + \frac{ba}{4} - \frac{b ^{2}}{4} + \frac{xg}{2} - \frac{a g}{4} + \frac{b g}{4}

e x p an d \frac{( 4 x ^{2} - x - 2 )}{x ( x ^{2} + 1 )}

e x p an d \frac{x ^{3} + 2 x ^{2}}{( x - 1 ) ^{2}}

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

\frac{d}{d t} ((P (t)) P (t) (1 - P (t)))

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