What is expand ((n+1)(2n+1))/3 ?

The solution to expand ((n+1)(2n+1))/3 is (2n^2)/3+n+1/3

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expand ((n+1)(2n+1))/3

expand

\frac{( n + 1 ) ( 2 n + 1 )}{3}

\frac{2 n ^{2}}{3} + n + \frac{1}{3}

Solution steps

\frac{( n + 1 ) ( 2 n + 1 )}{3}

Expand

(n + 1) (2 n + 1) : 2 n^{2} + 3 n + 1

= \frac{2 n ^{2} + 3 n + 1}{3}

Apply the fraction rule:

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

\frac{2 n ^{2} + 3 n + 1}{3} = \frac{2 n ^{2}}{3} + \frac{3 n}{3} + \frac{1}{3}

= \frac{2 n ^{2}}{3} + \frac{3 n}{3} + \frac{1}{3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{2 n ^{2}}{3} + n + \frac{1}{3}

sin ((a x - b t)^{2}) (a x - b t)

\frac{a ^{2}}{b ^{4} c}

- \frac{6 x}{( 3 x ^{2} + 4 ) ^{2}}

cos^{2} (x) (sec (x) - 1)

ln (\frac{( 2 x + 7 )}{y ^{3} + 3})

What is expand ((n+1)(2n+1))/3 ?
The solution to expand ((n+1)(2n+1))/3 is (2n^2)/3+n+1/3