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

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

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factor (x+y)^3-(x-y)^3

factor

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

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

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

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

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

(x + 1)^{2} + 3 (x + 1) - 4

4 (x + a) 2 - 49 y^{2}

(x + 1) - (3 x^{2})

4 x^{2} - 12 + 9

20 d^{2} - 45 e^{2}

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