9514 1404 393
Answer:
k = -2
Explanation:
The determinant can be formed by subtracting up-diagonal products from down-diagonal products:
(x)(x+y)(y) +(y)(x)(x+y) +(x+y)(y)(x) -(x+y)^3 -x^3 -y^3
= 3xy(x+y) -(x^3 +3x^2y +3xy^2 +y^3) -x^3 -y^3
= -2(x^3 +y^3)
The value of k is -2.