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

The solution to expand ((n+1)(n+2)(n+3))/3 is (n^3)/3+2n^2+(11n)/3+2

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

expand

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

\frac{n ^{3}}{3} + 2 n^{2} + \frac{11 n}{3} + 2

Solution steps

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

Expand

(n + 1) (n + 2) (n + 3) : n^{3} + 6 n^{2} + 11 n + 6

= \frac{n ^{3} + 6 n ^{2} + 11 n + 6}{3}

Apply the fraction rule:

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

\frac{n ^{3} + 6 n ^{2} + 11 n + 6}{3} = \frac{n ^{3}}{3} + \frac{6 n ^{2}}{3} + \frac{11 n}{3} + \frac{6}{3}

= \frac{n ^{3}}{3} + \frac{6 n ^{2}}{3} + \frac{11 n}{3} + \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= \frac{n ^{3}}{3} + 2 n^{2} + \frac{11 n}{3} + 2

(y^{2} + 1) d x - (x^{2} + 1) y d y

(5 - 2 x)^{2}

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

\frac{x}{( x - 3 ) ^{2}}

What is expand ((n+1)(n+2)(n+3))/3 ?
The solution to expand ((n+1)(n+2)(n+3))/3 is (n^3)/3+2n^2+(11n)/3+2