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

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

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

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

k^{3} + 3 k^{2} \cdot 1 + 3 k \cdot 1^{2} + 1^{3} : k^{3} + 3 k^{2} + 3 k + 1

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

\frac{2}{s ^{2} ( s + 2 )}

(sec (x) + csc (x)) (sin (x) + cos (x)) - 2 - cot (x)

sin (y) (x + sin (y)) d x + 2 x^{2} cos (y) d y

(2 + 3) (5 + 2)

cos (x) (sec (x) + csc (x))

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