What is expand (((n-1)(n)(2n-1)))/6 ?

The solution to expand (((n-1)(n)(2n-1)))/6 is (n^3)/3-(n^2)/2+n/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (((n-1)(n)(2n-1)))/6

expand

\frac{( ( n - 1 ) ( n ) ( 2 n - 1 ) )}{6}

\frac{n ^{3}}{3} - \frac{n ^{2}}{2} + \frac{n}{6}

Solution steps

\frac{( n - 1 ) ( n ) ( 2 n - 1 )}{6}

Remove parentheses:

(a) = a

= \frac{( n - 1 ) n ( 2 n - 1 )}{6}

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

\frac{2 n ^{3}}{6} : \frac{n ^{3}}{3}

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

Cancel

\frac{3 n ^{2}}{6} : \frac{n ^{2}}{2}

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

\frac{3 a}{( a + 1 ) ^{2}}

(1 + t y + y^{2}) d t + (1 + t y + t^{2}) d y

(x - π) (1 - cos (x))

P (0, - 3) y Q (2, 3)

(B + a t^{2}) (π r^{2} + 2 π cr t + π c^{2} t^{2})

What is expand (((n-1)(n)(2n-1)))/6 ?
The solution to expand (((n-1)(n)(2n-1)))/6 is (n^3)/3-(n^2)/2+n/6