What is (1/3 x-2/5 y)^3 ?

The solution to (1/3 x-2/5 y)^3 is (x^3)/(27)-(2x^2y)/(15)+(4xy^2)/(25)-(8y^3)/(125)

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simplify (1/3 x-2/5 y)^3

simplify

(\frac{1}{3} x - \frac{2}{5} y)^{3}

\frac{x ^{3}}{27} - \frac{2 x ^{2} y}{15} + \frac{4 x y ^{2}}{25} - \frac{8 y ^{3}}{125}

Solution steps

(\frac{1}{3} x - \frac{2}{5} y)^{3}

\frac{1}{3} x = \frac{x}{3}

\frac{2}{5} y = \frac{2 y}{5}

= (\frac{x}{3} - \frac{2 y}{5})^{3}

Apply Perfect Cube Formula:

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

a = \frac{x}{3}, b = \frac{2 y}{5}

= (\frac{x}{3})^{3} - 3 (\frac{x}{3})^{2} \frac{2 y}{5} + 3 \cdot \frac{x}{3} (\frac{2 y}{5})^{2} - (\frac{2 y}{5})^{3}

Simplify

(\frac{x}{3})^{3} - 3 (\frac{x}{3})^{2} \frac{2 y}{5} + 3 \cdot \frac{x}{3} (\frac{2 y}{5})^{2} - (\frac{2 y}{5})^{3} : \frac{x ^{3}}{27} - \frac{2 x ^{2} y}{15} + \frac{4 x y ^{2}}{25} - \frac{8 y ^{3}}{125}

= \frac{x ^{3}}{27} - \frac{2 x ^{2} y}{15} + \frac{4 x y ^{2}}{25} - \frac{8 y ^{3}}{125}

\frac{( ( 3 + h ) ^{4} - 81 )}{h}

(- 1 - 4) y (4.6)

0.4 \frac{m ^{3}}{s}

a (- 1.1) e b (2.7)

(1 - 2 x)^{- 1}

What is (1/3 x-2/5 y)^3 ?
The solution to (1/3 x-2/5 y)^3 is (x^3)/(27)-(2x^2y)/(15)+(4xy^2)/(25)-(8y^3)/(125)