What is (k^2(k+1)^2)/4+(k+1)^3 ?

The solution to (k^2(k+1)^2)/4+(k+1)^3 is (k^4+6k^3+13k^2+12k+4)/4

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simplify (k^2(k+1)^2)/4+(k+1)^3

simplify

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

\frac{k ^{4} + 6 k ^{3} + 13 k ^{2} + 12 k + 4}{4}

Solution steps

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

Apply the fraction rule:

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

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

Simplify

(k + 1)^{3} \cdot 4 + k^{2} (k + 1)^{2} : k^{4} + 6 k^{3} + 13 k^{2} + 12 k + 4

= \frac{k ^{4} + 6 k ^{3} + 13 k ^{2} + 12 k + 4}{4}

\frac{7}{35}

(- 2 x + 1) (- 4 x^{2} - 1)

(- 7 - 4 i) (- 12 - 7 i)

(7 - 2 i) - (- 11 + 6 i)

(2 x - 5 y)^{3}

What is (k^2(k+1)^2)/4+(k+1)^3 ?
The solution to (k^2(k+1)^2)/4+(k+1)^3 is (k^4+6k^3+13k^2+12k+4)/4