What is expand ((2n+1)^2)/8+(n+1) ?

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

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expand ((2n+1)^2)/8+(n+1)

expand

\frac{( 2 n + 1 ) ^{2}}{8} + (n + 1)

\frac{n ^{2}}{2} + \frac{n}{2} + \frac{1}{8} + n + 1

Solution steps

\frac{( 2 n + 1 ) ^{2}}{8} + (n + 1)

Remove parentheses:

(a) = a

= \frac{( 2 n + 1 ) ^{2}}{8} + n + 1

(2 n + 1)^{2} = 4 n^{2} + 4 n + 1

= \frac{4 n ^{2} + 4 n + 1}{8} + n + 1

Apply the fraction rule:

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

\frac{4 n ^{2} + 4 n + 1}{8} = \frac{4 n ^{2}}{8} + \frac{4 n}{8} + \frac{1}{8}

= \frac{4 n ^{2}}{8} + \frac{4 n}{8} + \frac{1}{8} + n + 1

Cancel

\frac{4 n ^{2}}{8} : \frac{n ^{2}}{2}

= \frac{n ^{2}}{2} + \frac{4 n}{8} + \frac{1}{8} + n + 1

Cancel

\frac{4 n}{8} : \frac{n}{2}

= \frac{n ^{2}}{2} + \frac{n}{2} + \frac{1}{8} + n + 1

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