The determinant y2−xyx2abca'b'c' is equal to

Let Δ=y2−xyx2abca'b'c'Then,Δ=1xyxy2−xyx2yaxbcya'xb'c'y           [Applying C1→xC1,C3→yC3] =1xy0−xy0ax+bybbx+cya'x+b'yb'b'x+c'y     [Applying C1→C1+yC2,C3→C3+xC2] =1xyxyax+bybx+cya'x+b'yb'x+c'y            [Expanding along R1] =ax+bybx+cya'x+b'yb'x+c'y