What is expand (2n-1/2)^3 ?

The solution to expand (2n-1/2)^3 is (64n^3-48n^2+12n-1)/8

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expand (2n-1/2)^3

expand

(2 n - \frac{1}{2})^{3}

\frac{64 n ^{3} - 48 n ^{2} + 12 n - 1}{8}

Solution steps

(2 n - \frac{1}{2})^{3}

Apply Perfect Cube Formula:

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

(2 n - \frac{1}{2})^{3} = (2 n)^{3} - 3 (2 n)^{2} \frac{1}{2} + 3 \cdot 2 n (\frac{1}{2})^{2} - (\frac{1}{2})^{3}

= (2 n)^{3} - 3 (2 n)^{2} \frac{1}{2} + 3 \cdot 2 n (\frac{1}{2})^{2} - (\frac{1}{2})^{3}

Simplify

(2 n)^{3} - 3 (2 n)^{2} \frac{1}{2} + 3 \cdot 2 n (\frac{1}{2})^{2} - (\frac{1}{2})^{3} : \frac{64 n ^{3} - 48 n ^{2} + 12 n - 1}{8}

= \frac{64 n ^{3} - 48 n ^{2} + 12 n - 1}{8}

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What is expand (2n-1/2)^3 ?
The solution to expand (2n-1/2)^3 is (64n^3-48n^2+12n-1)/8