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

The solution to expand (1/2 m-n)^3 is (m^3+12mn^2-6nm^2-8n^3)/8

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expand (1/2 m-n)^3

expand

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

\frac{m ^{3} + 12 m n ^{2} - 6 n m ^{2} - 8 n ^{3}}{8}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(\frac{1}{2} m)^{3} - 3 (\frac{1}{2} m)^{2} n + 3 \cdot \frac{1}{2} m n^{2} - n^{3} : \frac{m ^{3} + 12 m n ^{2} - 6 n m ^{2} - 8 n ^{3}}{8}

= \frac{m ^{3} + 12 m n ^{2} - 6 n m ^{2} - 8 n ^{3}}{8}

(x + y) y d x + (2 y + x - 1) d y

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

\frac{1}{2 j ( 4 + j ^{4} π )}

\frac{d}{d x} ((Q (x, y)) (x^{2} + y (x, d)^{2}) d y (x, d))

(e^{\frac{jπ}{2}} - e^{- \frac{jπ}{2}})^{3}

What is expand (1/2 m-n)^3 ?
The solution to expand (1/2 m-n)^3 is (m^3+12mn^2-6nm^2-8n^3)/8