erweitern ((9(12-3x-6y)^2))/(32)

Lösung

erweitern

\frac{( 9 ( 12 - 3 x - 6 y ) ^{2} )}{32}

\frac{81}{2} - \frac{81 x}{4} - \frac{81 y}{2} + \frac{81 x ^{2}}{32} + \frac{81 x y}{8} + \frac{81 y ^{2}}{8}

Schritte zur Lösung

\frac{9 ( 12 - 3 x - 6 y ) ^{2}}{32}

(12 - 3 x - 6 y)^{2} = 144 - 72 x - 144 y + 9 x^{2} + 36 x y + 36 y^{2}

= \frac{9 ( 9 x ^{2} + 36 x y - 72 x + 36 y ^{2} + 144 - 144 y )}{32}

Multipliziere aus

9 (144 - 72 x - 144 y + 9 x^{2} + 36 x y + 36 y^{2}) : 1296 - 648 x - 1296 y + 81 x^{2} + 324 x y + 324 y^{2}

= \frac{1296 - 648 x - 1296 y + 81 x ^{2} + 324 x y + 324 y ^{2}}{32}

Wende Bruchregel an:

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

\frac{1296 - 648 x - 1296 y + 81 x ^{2} + 324 x y + 324 y ^{2}}{32} = \frac{1296}{32} - \frac{648 x}{32} - \frac{1296 y}{32} + \frac{81 x ^{2}}{32} + \frac{324 x y}{32} + \frac{324 y ^{2}}{32}

= \frac{1296}{32} - \frac{648 x}{32} - \frac{1296 y}{32} + \frac{81 x ^{2}}{32} + \frac{324 x y}{32} + \frac{324 y ^{2}}{32}

\frac{1296}{32} = \frac{81}{2}

\frac{648 x}{32} = \frac{81 x}{4}

\frac{1296 y}{32} = \frac{81 y}{2}

\frac{324 x y}{32} = \frac{81 x y}{8}

\frac{324 y ^{2}}{32} = \frac{81 y ^{2}}{8}

= \frac{81}{2} - \frac{81 x}{4} - \frac{81 y}{2} + \frac{81 x ^{2}}{32} + \frac{81 x y}{8} + \frac{81 y ^{2}}{8}

e x p an d \frac{1}{3 x ^{2} - 3} - \frac{2}{2 x + 2} - \frac{x + 5}{x + 1}

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

e x p an d (2 r cos (θ) - r sin (θ)) r

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

e x p an d \frac{( e ^{\frac{y}{t}} )}{( e ^{\frac{y}{t}} ) ^{2}}