erweitern (b(-144+16x^2+9y^2)^2)/(20736)

Lösung

erweitern

\frac{b ( - 144 + 16 x ^{2} + 9 y ^{2} ) ^{2}}{20736}

b - \frac{2 b x ^{2}}{9} - \frac{b y ^{2}}{8} + \frac{b x ^{4}}{81} + \frac{b x ^{2} y ^{2}}{72} + \frac{b y ^{4}}{256}

Schritte zur Lösung

\frac{b ( - 144 + 16 x ^{2} + 9 y ^{2} ) ^{2}}{20736}

(- 144 + 16 x^{2} + 9 y^{2})^{2} = 20736 - 4608 x^{2} - 2592 y^{2} + 256 x^{4} + 288 x^{2} y^{2} + 81 y^{4}

= \frac{b ( 256 x ^{4} + 288 x ^{2} y ^{2} - 4608 x ^{2} + 81 y ^{4} + 20736 - 2592 y ^{2} )}{20736}

Multipliziere aus

b (20736 - 4608 x^{2} - 2592 y^{2} + 256 x^{4} + 288 x^{2} y^{2} + 81 y^{4}) : 20736 b - 4608 b x^{2} - 2592 b y^{2} + 256 b x^{4} + 288 b x^{2} y^{2} + 81 b y^{4}

= \frac{20736 b - 4608 b x ^{2} - 2592 b y ^{2} + 256 b x ^{4} + 288 b x ^{2} y ^{2} + 81 b y ^{4}}{20736}

Wende Bruchregel an:

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

\frac{20736 b - 4608 b x ^{2} - 2592 b y ^{2} + 256 b x ^{4} + 288 b x ^{2} y ^{2} + 81 b y ^{4}}{20736} = \frac{20736 b}{20736} - \frac{4608 b x ^{2}}{20736} - \frac{2592 b y ^{2}}{20736} + \frac{256 b x ^{4}}{20736} + \frac{288 b x ^{2} y ^{2}}{20736} + \frac{81 b y ^{4}}{20736}

= \frac{20736 b}{20736} - \frac{4608 b x ^{2}}{20736} - \frac{2592 b y ^{2}}{20736} + \frac{256 b x ^{4}}{20736} + \frac{288 b x ^{2} y ^{2}}{20736} + \frac{81 b y ^{4}}{20736}

\frac{20736 b}{20736} = b

\frac{4608 b x ^{2}}{20736} = \frac{2 b x ^{2}}{9}

\frac{2592 b y ^{2}}{20736} = \frac{b y ^{2}}{8}

\frac{256 b x ^{4}}{20736} = \frac{b x ^{4}}{81}

\frac{288 b x ^{2} y ^{2}}{20736} = \frac{b x ^{2} y ^{2}}{72}

\frac{81 b y ^{4}}{20736} = \frac{b y ^{4}}{256}

= b - \frac{2 b x ^{2}}{9} - \frac{b y ^{2}}{8} + \frac{b x ^{4}}{81} + \frac{b x ^{2} y ^{2}}{72} + \frac{b y ^{4}}{256}

e x p an d H (- 3.6) U (7, - 4)

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

e x p an d (e^{x} - 2) (e^{x} - 3)

s im pl i f y s (s + 5) (s + \frac{1}{60})

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