Evaluate 
Let Δ = 
Applying Elementary Transformations.
Applying R1→ R1 + R2 + R3, we have
Δ = 
Δ = 2 (x + y)
Applying C2→ C2 – C1 and C3→ C3 – C1, we have
Δ = 2 (x + y)
Expanding along R1, we have
Δ = 2 (x + y) [1 (x × (-x) – (-y) × (x – y)) – 0 + 0]
Δ = 2 (x + y) [-x2 + y (x – y)]
Δ = 2 (x + y) [-x2 + xy – y2]
Δ = -2 (x + y) [x2 – xy + y2]
Δ = -2 (x3 + y3)
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