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

The solution to (2/3 x^2-3/2 y)^3 is (8x^6}{27}-2x^4y+\frac{9x^2y^2)/2-(27y^3)/8

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

simplify

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

\frac{8 x ^{6}}{27} - 2 x^{4} y + \frac{9 x ^{2} y ^{2}}{2} - \frac{27 y ^{3}}{8}

Solution steps

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

Multiply

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

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

Multiply

\frac{3}{2} y : \frac{3 y}{2}

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

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

Simplify

(\frac{2 x ^{2}}{3})^{3} - 3 (\frac{2 x ^{2}}{3})^{2} \frac{3 y}{2} + 3 \cdot \frac{2 x ^{2}}{3} (\frac{3 y}{2})^{2} - (\frac{3 y}{2})^{3} : \frac{8 x ^{6}}{27} - 2 x^{4} y + \frac{9 x ^{2} y ^{2}}{2} - \frac{27 y ^{3}}{8}

= \frac{8 x ^{6}}{27} - 2 x^{4} y + \frac{9 x ^{2} y ^{2}}{2} - \frac{27 y ^{3}}{8}

(x + 3)^{2} - (x - 2)^{2}

(\frac{3}{5 \cdot x ^{n} + 2}) \cdot x^{2} + x^{n} \cdot (1 x + 2)

\frac{( 0.6 a ^{4} \cdot b ^{3} \cdot c ^{2} )}{( 0.3 a \cdot b ^{5} \cdot c ^{7} )}

3 x^{2} - 5^{x} + 1 \cdot 2^{2} x

(n + 1)^{2} - 2 (n + 2)

What is (2/3 x^2-3/2 y)^3 ?
The solution to (2/3 x^2-3/2 y)^3 is (8x^6}{27}-2x^4y+\frac{9x^2y^2)/2-(27y^3)/8