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

The solution to (1/2 x-1/3 y)^3 is (x^3)/8-(x^2y)/4+(xy^2)/6-(y^3)/(27)

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

simplify

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

\frac{x ^{3}}{8} - \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} - \frac{y ^{3}}{27}

Solution steps

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

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

\frac{1}{3} y = \frac{y}{3}

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

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

Simplify

(\frac{x}{2})^{3} - 3 (\frac{x}{2})^{2} \frac{y}{3} + 3 \cdot \frac{x}{2} (\frac{y}{3})^{2} - (\frac{y}{3})^{3} : \frac{x ^{3}}{8} - \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} - \frac{y ^{3}}{27}

= \frac{x ^{3}}{8} - \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} - \frac{y ^{3}}{27}

(8 y + y^{2})^{3}

- 16 a^{4} b^{6} - 24 a^{5} b^{5} - 9 a^{6} b^{4}

(2 x + 3) \cdot 0.4 x

\frac{( 6 y ^{3} ) ^{3}}{2 y ^{5}}

a^{9} - b^{9}

What is (1/2 x-1/3 y)^3 ?
The solution to (1/2 x-1/3 y)^3 is (x^3)/8-(x^2y)/4+(xy^2)/6-(y^3)/(27)