What is expand (n(2n+1)(4n+1))/3 ?

The solution to expand (n(2n+1)(4n+1))/3 is (8n^3)/3+2n^2+n/3

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expand (n(2n+1)(4n+1))/3

expand

\frac{n ( 2 n + 1 ) ( 4 n + 1 )}{3}

\frac{8 n ^{3}}{3} + 2 n^{2} + \frac{n}{3}

Solution steps

\frac{n ( 2 n + 1 ) ( 4 n + 1 )}{3}

Expand

n (2 n + 1) (4 n + 1) : 8 n^{3} + 6 n^{2} + n

= \frac{8 n ^{3} + 6 n ^{2} + n}{3}

Apply the fraction rule:

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

\frac{8 n ^{3} + 6 n ^{2} + n}{3} = \frac{8 n ^{3}}{3} + \frac{6 n ^{2}}{3} + \frac{n}{3}

= \frac{8 n ^{3}}{3} + \frac{6 n ^{2}}{3} + \frac{n}{3}

Divide the numbers:

\frac{6}{3} = 2

= \frac{8 n ^{3}}{3} + 2 n^{2} + \frac{n}{3}

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

(f \circ g) (2 - 8 x) (x^{3})

\frac{5}{s ( s ^{2} + 5 s + 50 )}

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

(3 x - y = 30,) (4 x + 3 y = 1)

What is expand (n(2n+1)(4n+1))/3 ?
The solution to expand (n(2n+1)(4n+1))/3 is (8n^3)/3+2n^2+n/3