What is expand (n+5k)^3 ?

The solution to expand (n+5k)^3 is n^3+15n^2k+75nk^2+125k^3

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expand (n+5k)^3

expand

(n + 5 k)^{3}

n^{3} + 15 n^{2} k + 75 n k^{2} + 125 k^{3}

Solution steps

(n + 5 k)^{3}

Apply Perfect Cube Formula:

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

(n + 5 k)^{3} = n^{3} + 3 n^{2} \cdot 5 k + 3 n (5 k)^{2} + (5 k)^{3}

= n^{3} + 3 n^{2} \cdot 5 k + 3 n (5 k)^{2} + (5 k)^{3}

Simplify

n^{3} + 3 n^{2} \cdot 5 k + 3 n (5 k)^{2} + (5 k)^{3} : n^{3} + 15 n^{2} k + 75 n k^{2} + 125 k^{3}

= n^{3} + 15 n^{2} k + 75 n k^{2} + 125 k^{3}

\frac{x + 3}{x ^{3} + 27}

(x - 1) (x - 2) (x - 5)

\frac{x ^{2} - 2 x}{x}

(- 2 + 2 i)^{4}

4 sin^{2} (t) + 4 cos^{2} (t)

What is expand (n+5k)^3 ?
The solution to expand (n+5k)^3 is n^3+15n^2k+75nk^2+125k^3