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

The solution to expand (2n(n+1)(2n+1))/3 is (4n^3)/3+2n^2+(2n)/3

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

expand

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

\frac{4 n ^{3}}{3} + 2 n^{2} + \frac{2 n}{3}

Solution steps

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

Expand

2 n (n + 1) (2 n + 1) : 4 n^{3} + 6 n^{2} + 2 n

= \frac{4 n ^{3} + 6 n ^{2} + 2 n}{3}

Apply the fraction rule:

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

\frac{4 n ^{3} + 6 n ^{2} + 2 n}{3} = \frac{4 n ^{3}}{3} + \frac{6 n ^{2}}{3} + \frac{2 n}{3}

= \frac{4 n ^{3}}{3} + \frac{6 n ^{2}}{3} + \frac{2 n}{3}

Divide the numbers:

\frac{6}{3} = 2

= \frac{4 n ^{3}}{3} + 2 n^{2} + \frac{2 n}{3}

(4 d - 3 e)^{5}

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

- \frac{42 x ^{5} ( x + 1 )}{55 y ^{2}}

\frac{15}{x ( x - 5 )}

(e^{x} - 5)^{3}

What is expand (2n(n+1)(2n+1))/3 ?
The solution to expand (2n(n+1)(2n+1))/3 is (4n^3)/3+2n^2+(2n)/3