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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{6}{3} = 2

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

(cos (x) + i sin (x))^{2}

(cos (x) + i sin (x))^{5}

(x + y i)^{4}

(3 + i)^{7}

(x + 2)^{2}

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