erweitern ((a-bc)^2)/(4n^2)

Lösung

erweitern

\frac{( a - b c ) ^{2}}{4 n ^{2}}

\frac{a ^{2}}{4 n ^{2}} - \frac{ab c}{2 n ^{2}} + \frac{b ^{2} c ^{2}}{4 n ^{2}}

Schritte zur Lösung

\frac{( a - b c ) ^{2}}{4 n ^{2}}

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

= \frac{a ^{2} - 2 ab c + b ^{2} c ^{2}}{4 n ^{2}}

Wende Bruchregel an:

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

\frac{a ^{2} - 2 ab c + b ^{2} c ^{2}}{4 n ^{2}} = \frac{a ^{2}}{4 n ^{2}} - \frac{2 ab c}{4 n ^{2}} + \frac{b ^{2} c ^{2}}{4 n ^{2}}

= \frac{a ^{2}}{4 n ^{2}} - \frac{2 ab c}{4 n ^{2}} + \frac{b ^{2} c ^{2}}{4 n ^{2}}

Streiche

\frac{2 ab c}{4 n ^{2}} : \frac{ab c}{2 n ^{2}}

= \frac{a ^{2}}{4 n ^{2}} - \frac{ab c}{2 n ^{2}} + \frac{b ^{2} c ^{2}}{4 n ^{2}}

e x p an d (2 + 5 = 6,) v (5 - 3 = 4)

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e x p an d \frac{12 e ^{- 2 s} + 12 e ^{- 5 s} + 3 s}{s ( 3 + s )}

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