erweitern ((a-b)^2)/(2b)

Lösung

erweitern

\frac{( a - b ) ^{2}}{2 b}

\frac{a ^{2}}{2 b} - a + \frac{b}{2}

Schritte zur Lösung

\frac{( a - b ) ^{2}}{2 b}

(a - b)^{2} = a^{2} - 2 ab + b^{2}

= \frac{a ^{2} - 2 ab + b ^{2}}{2 b}

Wende Bruchregel an:

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

\frac{a ^{2} - 2 ab + b ^{2}}{2 b} = \frac{a ^{2}}{2 b} - \frac{2 ab}{2 b} + \frac{b ^{2}}{2 b}

= \frac{a ^{2}}{2 b} - \frac{2 ab}{2 b} + \frac{b ^{2}}{2 b}

Streiche

\frac{2 ab}{2 b} : a

= \frac{a ^{2}}{2 b} - a + \frac{b ^{2}}{2 b}

Streiche

\frac{b ^{2}}{2 b} : \frac{b}{2}

= \frac{a ^{2}}{2 b} - a + \frac{b}{2}

e x p an d 936 \cdot 4

e x p an d \frac{8 ( x + 1 )}{x ^{2}}

e x p an d (e^{- x} - 1) (e^{- x} + 1)

e x p an d e v a l u a t e (10 - 4 i) + (5 + i)

e x p an d i (- 4, 5) j (- 4, - 3) k (5, - 8) l (5, 0)