What is (1/2*x-2/3*y)^3 ?

The solution to (1/2*x-2/3*y)^3 is (x^3)/8-(x^2y)/2+(2xy^2)/3-(8y^3)/(27)

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simplify (1/2x-2/3y)^3

simplify

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

\frac{x ^{3}}{8} - \frac{x ^{2} y}{2} + \frac{2 x y ^{2}}{3} - \frac{8 y ^{3}}{27}

Solution steps

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

\frac{1}{2} x = \frac{x}{2}

\frac{2}{3} y = \frac{2 y}{3}

= (\frac{x}{2} - \frac{2 y}{3})^{3}

Apply Perfect Cube Formula:

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

a = \frac{x}{2}, b = \frac{2 y}{3}

= (\frac{x}{2})^{3} - 3 (\frac{x}{2})^{2} \frac{2 y}{3} + 3 \cdot \frac{x}{2} (\frac{2 y}{3})^{2} - (\frac{2 y}{3})^{3}

Simplify

(\frac{x}{2})^{3} - 3 (\frac{x}{2})^{2} \frac{2 y}{3} + 3 \cdot \frac{x}{2} (\frac{2 y}{3})^{2} - (\frac{2 y}{3})^{3} : \frac{x ^{3}}{8} - \frac{x ^{2} y}{2} + \frac{2 x y ^{2}}{3} - \frac{8 y ^{3}}{27}

= \frac{x ^{3}}{8} - \frac{x ^{2} y}{2} + \frac{2 x y ^{2}}{3} - \frac{8 y ^{3}}{27}

30 v^{7} w^{9} + 24 v w^{4} y^{3}

28 b + 12

625 a^{4} - 256 b^{4}

x^{6} + 216

64 - 343 x^{3}

What is (1/2*x-2/3*y)^3 ?
The solution to (1/2*x-2/3*y)^3 is (x^3)/8-(x^2y)/2+(2xy^2)/3-(8y^3)/(27)