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

The solution to (2/3*x^2-1/2*y)^3 is (8x^6}{27}-\frac{2x^4y)/3+(x^2y^2)/2-(y^3)/8

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

simplify

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

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

Solution steps

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

\frac{2}{3} x^{2} = \frac{2 x ^{2}}{3}

\frac{1}{2} y = \frac{y}{2}

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

\frac{( p ^{2} )}{9 - 36}

x^{2} - 6 x y - 40 y^{2}

(\frac{- 1}{10})^{x}

\frac{f ^{''} ( 1 ) ln ( x ^{2} )}{e ^{2} x}

(5 x - 2 x) 2

What is (2/3*x^2-1/2*y)^3 ?
The solution to (2/3*x^2-1/2*y)^3 is (8x^6}{27}-\frac{2x^4y)/3+(x^2y^2)/2-(y^3)/8