erweitern ((a+b)(6a-ab+6b))/(27)

Lösung

erweitern

\frac{( a + b ) ( 6 a - ab + 6 b )}{27}

\frac{2 a ^{2}}{9} - \frac{a ^{2} b}{27} + \frac{4 ab}{9} - \frac{a b ^{2}}{27} + \frac{2 b ^{2}}{9}

Schritte zur Lösung

\frac{( a + b ) ( 6 a - ab + 6 b )}{27}

Multipliziere aus

(a + b) (6 a - ab + 6 b) : 6 a^{2} - a^{2} b + 12 ab - a b^{2} + 6 b^{2}

= \frac{6 a ^{2} - a ^{2} b + 12 ab - a b ^{2} + 6 b ^{2}}{27}

Wende Bruchregel an:

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

\frac{6 a ^{2} - a ^{2} b + 12 ab - a b ^{2} + 6 b ^{2}}{27} = \frac{6 a ^{2}}{27} - \frac{a ^{2} b}{27} + \frac{12 ab}{27} - \frac{a b ^{2}}{27} + \frac{6 b ^{2}}{27}

= \frac{6 a ^{2}}{27} - \frac{a ^{2} b}{27} + \frac{12 ab}{27} - \frac{a b ^{2}}{27} + \frac{6 b ^{2}}{27}

Streiche

\frac{6 a ^{2}}{27} : \frac{2 a ^{2}}{9}

= \frac{2 a ^{2}}{9} - \frac{a ^{2} b}{27} + \frac{12 ab}{27} - \frac{a b ^{2}}{27} + \frac{6 b ^{2}}{27}

Streiche

\frac{12 ab}{27} : \frac{4 ab}{9}

= \frac{2 a ^{2}}{9} - \frac{a ^{2} b}{27} + \frac{4 ab}{9} - \frac{a b ^{2}}{27} + \frac{6 b ^{2}}{27}

Streiche

\frac{6 b ^{2}}{27} : \frac{2 b ^{2}}{9}

= \frac{2 a ^{2}}{9} - \frac{a ^{2} b}{27} + \frac{4 ab}{9} - \frac{a b ^{2}}{27} + \frac{2 b ^{2}}{9}

e x p an d y d x + (2 x y - x) d y

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