What is expand (2^r(r^2-2))/((r+1)^2(r+2)^2) ?

The solution to expand (2^r(r^2-2))/((r+1)^2(r+2)^2) is (2^rr^2-2^{1+r})/(r^4+6r^3+13r^2+12r+4)

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

expand

\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}

Solution steps

\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 )}

Expand

(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}

Expand

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}

\frac{( 4 x - 1 ) ^{2}}{4}

y \cdot (b^{2} - y^{2})

\frac{2 x ^{2} - 13 x + 20}{( x - 1 ) ^{2}}

π (\frac{2}{2 π})^{2}

(sec (x) - 1)^{3}

What is expand (2^r(r^2-2))/((r+1)^2(r+2)^2) ?
The solution to expand (2^r(r^2-2))/((r+1)^2(r+2)^2) is (2^rr^2-2^{1+r})/(r^4+6r^3+13r^2+12r+4)