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

The solution to expand (1/3 x+2/3 y)^2(x-y) is (x^3-4y^3+3x^2y)/9

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expand (1/3 x+2/3 y)^2(x-y)

expand

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

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

Solution steps

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

Expand

(\frac{1}{3} x + \frac{2}{3} y)^{2} : \frac{x ^{2} + 4 x y + 4 y ^{2}}{9}

= \frac{x ^{2} + 4 x y + 4 y ^{2}}{9} (x - y)

Apply the distributive law:

a (b - c) = ab - a c

\frac{x ^{2} + 4 x y + 4 y ^{2}}{9} (x - y) = \frac{x ^{2} + 4 x y + 4 y ^{2}}{9} x - \frac{x ^{2} + 4 x y + 4 y ^{2}}{9} y

= \frac{x ^{2} + 4 x y + 4 y ^{2}}{9} x - \frac{x ^{2} + 4 x y + 4 y ^{2}}{9} y

Simplify

\frac{x ^{2} + 4 x y + 4 y ^{2}}{9} x - \frac{x ^{2} + 4 x y + 4 y ^{2}}{9} y : \frac{x ^{3} - 4 y ^{3} + 3 x ^{2} y}{9}

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

\frac{1 - e ^{- 12 s}}{s ( s ^{2} + 1 )}

(2 + 3 x - 7)^{2}

\frac{2 + 7 x}{( 1 + 2 x ) ( 1 - x )}

\frac{b ^{2} - x ^{2}}{( b ^{2} + x ^{2} ) ^{2}}

\frac{173}{12} x - 16 (x - 4)

What is expand (1/3 x+2/3 y)^2(x-y) ?
The solution to expand (1/3 x+2/3 y)^2(x-y) is (x^3-4y^3+3x^2y)/9