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

The solution to (x-y)^3+(y-2)^3+(2-x)^3 is -3x^2y+3xy^2-12x-6y^2+6x^2+12y

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

simplify

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

- 3 x^{2} y + 3 x y^{2} - 12 x - 6 y^{2} + 6 x^{2} + 12 y

Solution steps

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

Expand

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

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

Expand

(y - 2)^{3} : y^{3} - 6 y^{2} + 12 y - 8

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} + y^{3} - 6 y^{2} + 12 y - 8 + (2 - x)^{3}

Expand

(2 - x)^{3} : 8 - 12 x + 6 x^{2} - x^{3}

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} + y^{3} - 6 y^{2} + 12 y - 8 + 8 - 12 x + 6 x^{2} - x^{3}

Add similar elements:

- y^{3} + y^{3} = 0

= x^{3} - 3 x^{2} y + 3 x y^{2} - 6 y^{2} + 12 y - 8 + 8 - 12 x + 6 x^{2} - x^{3}

Group like terms

= x^{3} - x^{3} - 3 x^{2} y + 3 x y^{2} - 12 x - 6 y^{2} + 6 x^{2} + 12 y - 8 + 8

Add similar elements:

x^{3} - x^{3} = 0

= - 3 x^{2} y + 3 x y^{2} - 12 x - 6 y^{2} + 6 x^{2} + 12 y - 8 + 8

Add the numbers:

- 8 + 8 = 0

= - 3 x^{2} y + 3 x y^{2} - 12 x - 6 y^{2} + 6 x^{2} + 12 y

(a + b)^{19}

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

(5 x^{2} + 7 y^{3})^{3}

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

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

What is (x-y)^3+(y-2)^3+(2-x)^3 ?
The solution to (x-y)^3+(y-2)^3+(2-x)^3 is -3x^2y+3xy^2-12x-6y^2+6x^2+12y