erweitern ((m-n)^2+6(m-n))/9

Lösung

erweitern

\frac{( m - n ) ^{2} + 6 ( m - n )}{9}

\frac{m ^{2}}{9} - \frac{2 mn}{9} + \frac{n ^{2}}{9} + \frac{2 m}{3} - \frac{2 n}{3}

Schritte zur Lösung

\frac{( m - n ) ^{2} + 6 ( m - n )}{9}

Multipliziere aus

(m - n)^{2} + 6 (m - n) : m^{2} - 2 mn + n^{2} + 6 m - 6 n

= \frac{m ^{2} - 2 mn + n ^{2} + 6 m - 6 n}{9}

Wende Bruchregel an:

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

\frac{m ^{2} - 2 mn + n ^{2} + 6 m - 6 n}{9} = \frac{m ^{2}}{9} - \frac{2 mn}{9} + \frac{n ^{2}}{9} + \frac{6 m}{9} - \frac{6 n}{9}

= \frac{m ^{2}}{9} - \frac{2 mn}{9} + \frac{n ^{2}}{9} + \frac{6 m}{9} - \frac{6 n}{9}

Streiche

\frac{6 m}{9} : \frac{2 m}{3}

= \frac{m ^{2}}{9} - \frac{2 mn}{9} + \frac{n ^{2}}{9} + \frac{2 m}{3} - \frac{6 n}{9}

Streiche

\frac{6 n}{9} : \frac{2 n}{3}

= \frac{m ^{2}}{9} - \frac{2 mn}{9} + \frac{n ^{2}}{9} + \frac{2 m}{3} - \frac{2 n}{3}

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

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

e x p an d (1, - 1) y (1, 5)

s im pl i f y e^{- 2 l n (\frac{1}{5})}

s im pl i f y (3 x^{4} y^{7}) (5 x^{2} y)