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Popular >

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

Solution

expand

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

Solution

\frac{k ^{3}}{3} + k^{2} + k + \frac{1}{3}

Solution steps

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

(k + 1)^{3} = k^{3} + 3 k^{2} + 3 k + 1

= \frac{k ^{3} + 3 k ^{2} + 3 k + 1}{3}

Apply the fraction rule:

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

\frac{k ^{3} + 3 k ^{2} + 3 k + 1}{3} = \frac{k ^{3}}{3} + \frac{3 k ^{2}}{3} + \frac{3 k}{3} + \frac{1}{3}

= \frac{k ^{3}}{3} + \frac{3 k ^{2}}{3} + \frac{3 k}{3} + \frac{1}{3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{k ^{3}}{3} + k^{2} + k + \frac{1}{3}

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Frequently Asked Questions (FAQ)

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