What is (x+y)^3-(x-y)^3-6y(x^2-y^2) ?

The solution to (x+y)^3-(x-y)^3-6y(x^2-y^2) is 8y^3

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simplify (x+y)^3-(x-y)^3-6y(x^2-y^2)

simplify

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

8 y^{3}

Solution steps

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

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} - (x - y)^{3} - 6 y (x^{2} - y^{2})

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

Expand

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

3 x^{2} y + 3 x^{2} y - 6 x^{2} y = 0

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

Add similar elements:

3 x y^{2} - 3 x y^{2} = 0

= y^{3} + y^{3} + 6 y^{3}

Add similar elements:

y^{3} + y^{3} + 6 y^{3} = 8 y^{3}

= 8 y^{3}

\frac{( ( y - 2 ) ( y - 3 ) )}{- 4} \cdot \frac{( - 4 y )}{( y - 2 )}

\frac{- 1}{a ^{b}}

\frac{( 5 - 80 x ^{2} )}{10}

(x + y + z)^{3} - (x - y - z)^{3} - 6 (x + y + z) (x - y - z) (y + z)

(m^{8} n^{4})^{4}

What is (x+y)^3-(x-y)^3-6y(x^2-y^2) ?
The solution to (x+y)^3-(x-y)^3-6y(x^2-y^2) is 8y^3