What is expand (4(n+1)(2n+1))/(n^2) ?

The solution to expand (4(n+1)(2n+1))/(n^2) is 8+(12)/n+4/(n^2)

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expand (4(n+1)(2n+1))/(n^2)

expand

\frac{4 ( n + 1 ) ( 2 n + 1 )}{n ^{2}}

8 + \frac{12}{n} + \frac{4}{n ^{2}}

Solution steps

\frac{4 ( n + 1 ) ( 2 n + 1 )}{n ^{2}}

Expand

4 (n + 1) (2 n + 1) : 8 n^{2} + 12 n + 4

= \frac{8 n ^{2} + 12 n + 4}{n ^{2}}

Apply the fraction rule:

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

\frac{8 n ^{2} + 12 n + 4}{n ^{2}} = \frac{8 n ^{2}}{n ^{2}} + \frac{12 n}{n ^{2}} + \frac{4}{n ^{2}}

= \frac{8 n ^{2}}{n ^{2}} + \frac{12 n}{n ^{2}} + \frac{4}{n ^{2}}

Cancel

\frac{8 n ^{2}}{n ^{2}} : 8

= 8 + \frac{12 n}{n ^{2}} + \frac{4}{n ^{2}}

Cancel

\frac{12 n}{n ^{2}} : \frac{12}{n}

= 8 + \frac{12}{n} + \frac{4}{n ^{2}}

4 sin^{2} (2 t) + 4 cos^{2} (2 t) + (e^{t} - e^{- t})^{2}

(x^{2} y^{3} - 4 y + 4 x - 3) d x + (3 x^{2} y^{2} - 4 x) d y

\Rightarrow 2 (x^{4} - 2 x^{3} + 4 x^{2} - 7 x - 34)

6 (1 - x - \frac{1 - x ^{2}}{2})

\frac{( 1 - e ^{- 2 (s - 1)} )}{( s - 1 ) ( s ^{2} + 2 s + 2 )}

What is expand (4(n+1)(2n+1))/(n^2) ?
The solution to expand (4(n+1)(2n+1))/(n^2) is 8+(12)/n+4/(n^2)