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Popular >

expand (4(k+1)^3)/k

Solution

expand

\frac{4 ( k + 1 ) ^{3}}{k}

Solution

4 k^{2} + 12 k + 12 + \frac{4}{k}

Solution steps

\frac{4 ( k + 1 ) ^{3}}{k}

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

= \frac{4 ( k ^{3} + 3 k ^{2} + 3 k + 1 )}{k}

Expand

4 (k^{3} + 3 k^{2} + 3 k + 1) : 4 k^{3} + 12 k^{2} + 12 k + 4

= \frac{4 k ^{3} + 12 k ^{2} + 12 k + 4}{k}

Apply the fraction rule:

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

\frac{4 k ^{3} + 12 k ^{2} + 12 k + 4}{k} = \frac{4 k ^{3}}{k} + \frac{12 k ^{2}}{k} + \frac{12 k}{k} + \frac{4}{k}

= \frac{4 k ^{3}}{k} + \frac{12 k ^{2}}{k} + \frac{12 k}{k} + \frac{4}{k}

Cancel

\frac{4 k ^{3}}{k} : 4 k^{2}

= 4 k^{2} + \frac{12 k ^{2}}{k} + \frac{12 k}{k} + \frac{4}{k}

Cancel

\frac{12 k ^{2}}{k} : 12 k

= 4 k^{2} + 12 k + \frac{12 k}{k} + \frac{4}{k}

Cancel

\frac{12 k}{k} : 12

= 4 k^{2} + 12 k + 12 + \frac{4}{k}

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Frequently Asked Questions (FAQ)

What is expand (4(k+1)^3)/k ?
The solution to expand (4(k+1)^3)/k is 4k^2+12k+12+4/k