Factorize (x+4)^3 - (x-y)^3

Dear Student,

{(x + 4)}^{3} - {(x - y)}^{3} = (x^{3} + 64 + 12 x (x + 4)) - (x^{3} - y^{3} - 3 x y (x - y)) = (x^{3} + 64 + 12 x^{2} + 48 x) - (x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2}) = x^{3} + 12 x^{2} + 48 x + 64 - x^{3} + y^{3} + 3 x^{2} y - 3 x y^{2} = y^{3} + 12 x^{2} + 3 x^{2} y + 48 x - 3 x y^{2} + 64 = y^{3} + 3 x^{2} (4 + y) + 3 x (16 - y^{2}) + 64 = 3 x^{2} (4 + y) + 3 x (16 - y^{2}) + (64 + y^{3}) = 3 x^{2} (4 + y) + 3 x (4^{2} - y^{2}) + (4^{3} + y^{3}) a^{2} - b^{2} = (a + b) (a - b) a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2}) = 3 x^{2} (4 + y) + 3 x (4 + y) (4 - y) + (4 + y) (y^{2} - 4 y + 16) = (y + 4) [3 x^{2} + 3 x (4 - y) + (y^{2} - 4 y + 16)]

Regards.