What is expand (9(n+1)(2n+1))/(2n^2) ?

The solution to expand (9(n+1)(2n+1))/(2n^2) is 9+(27)/(2n)+9/(2n^2)

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expand (9(n+1)(2n+1))/(2n^2)

expand

\frac{9 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

9 + \frac{27}{2 n} + \frac{9}{2 n ^{2}}

Solution steps

\frac{9 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

Expand

9 (n + 1) (2 n + 1) : 18 n^{2} + 27 n + 9

= \frac{18 n ^{2} + 27 n + 9}{2 n ^{2}}

Apply the fraction rule:

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

\frac{18 n ^{2} + 27 n + 9}{2 n ^{2}} = \frac{18 n ^{2}}{2 n ^{2}} + \frac{27 n}{2 n ^{2}} + \frac{9}{2 n ^{2}}

= \frac{18 n ^{2}}{2 n ^{2}} + \frac{27 n}{2 n ^{2}} + \frac{9}{2 n ^{2}}

Cancel

\frac{18 n ^{2}}{2 n ^{2}} : 9

= 9 + \frac{27 n}{2 n ^{2}} + \frac{9}{2 n ^{2}}

Cancel

\frac{27 n}{2 n ^{2}} : \frac{27}{2 n}

= 9 + \frac{27}{2 n} + \frac{9}{2 n ^{2}}

(2 x - 3)^{2}

(5, - 2) y (3, - 6)

(x - 2) (x + 2) (x^{2} - 2)

(2 + 3)^{2} - (2 - 3)^{2}

What is expand (9(n+1)(2n+1))/(2n^2) ?
The solution to expand (9(n+1)(2n+1))/(2n^2) is 9+(27)/(2n)+9/(2n^2)