What is expand (k^2(k+1)^2)/4+(k+1) ?

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

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expand (k^2(k+1)^2)/4+(k+1)

expand

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

\frac{k ^{4}}{4} + \frac{k ^{3}}{2} + \frac{k ^{2}}{4} + k + 1

Solution steps

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

Remove parentheses:

(a) = a

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

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

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