erweitern (2^r(r^2-2))/((r+1)^2(r+2)^2)

Lösung

erweitern

\frac{2 ^{r} ( r ^{2} - 2 )}{( r + 1 ) ^{2} ( r + 2 ) ^{2}}

\frac{2 ^{r} r ^{2} - 2 ^{1 + r}}{r ^{4} + 6 r ^{3} + 13 r ^{2} + 12 r + 4}

Schritte zur Lösung

\frac{2 ^{r} ( r ^{2} - 2 )}{( r + 1 ) ^{2} ( r + 2 ) ^{2}}

(r + 1)^{2} = r^{2} + 2 r + 1

= \frac{2 ^{r} ( r ^{2} - 2 )}{( r ^{2} + 2 r + 1 ) ( r + 2 ) ^{2}}

(r + 2)^{2} = r^{2} + 4 r + 4

= \frac{2 ^{r} ( r ^{2} - 2 )}{( r ^{2} + 2 r + 1 ) ( r ^{2} + 4 r + 4 )}

Multipliziere aus

(r^{2} + 2 r + 1) (r^{2} + 4 r + 4) : r^{4} + 6 r^{3} + 13 r^{2} + 12 r + 4

= \frac{2 ^{r} ( r ^{2} - 2 )}{r ^{4} + 6 r ^{3} + 13 r ^{2} + 12 r + 4}

Multipliziere aus

2^{r} (r^{2} - 2) : 2^{r} r^{2} - 2^{1 + r}

= \frac{2 ^{r} r ^{2} - 2 ^{r + 1}}{r ^{4} + 6 r ^{3} + 13 r ^{2} + 12 r + 4}

e x p an d \frac{( 4 x - 1 ) ^{2}}{4}

e x p an d y \cdot (b^{2} - y^{2})

e x p an d \frac{2 x ^{2} - 13 x + 20}{( x - 1 ) ^{2}}

e x p an d π (\frac{2}{2 π})^{2}

e x p an d (sec (x) - 1)^{3}