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

The solution to factor (x+2y)^3-(2x-y)^3 is (-x+3y)(7x^2+3xy+3y^2)

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

factor

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

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

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

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

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

2 am - 2 an + 2 a - (m - n + 1)

(x - 2) - (4 x^{2})

4 x^{2} - k \cdot x + 2 k - 16

(x + y)^{2} - 6 (x + y) + 9

2 - 121

What is factor (x+2y)^3-(2x-y)^3 ?
The solution to factor (x+2y)^3-(2x-y)^3 is (-x+3y)(7x^2+3xy+3y^2)