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Question
Evaluate `|(x, y, x+y),(y, x+y, x),(x+y, x, y)|`
Solution
Let, Δ = `[(x,y,x+y),(y,x+y,x),(x+y,x,y)]`
= `[(2(x + y),y,x+y),(2(x + y), x+y,x),(2(x + y),x,y)],[C_1 → C_1 + C_2 + C_3]`
= `2(x + y)[(1,y,x+y),(1,x+y,x),(1,x,y)]`
Δ = `2(x + y)[(1,y,x+y),(0,x,-y),(0,x-y,-x)] [R_2 → R_2 - R_1 "and" R_3 → R_3 - R_1]`
= `2(x + y)[(x,-y),(x-y,-x)] = 2(x + y)[-x^2 + y(x - y)]`
= `2(x + y)[-x^2 + xy - y^2]`
= `-2(x + y)[x^2 + y^2 - xy]`
= `-2(x^3 + y^3)`
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