Để đơn giản, Anh viết x∼x2;y∼y2;z∼z2;a∼a2;b∼b2.Ta có:
xyzab+(x−a)(y−a)(z−a)a(a−b)+(x−b)(y−b)(z−b)b(b−a)
=xyzab+xyz−a(xy+yz+zx)+a2(x+y+z)−a3a(a−b)−xyz−b(xy+yz+zx)+b2(x+y+z)−b3b(a−b)
=xyz(1ab+1a(a−b)−1b(a−b))−xy+yz+zxa−b+xy+yz+zxa−b+x+y+za−b(a−b)−a2a−b+b2a−b
=xyz(a−b+b−aab(a−b))+0+x+y+z−a2−b2a−b
=0+0+x+y+z−(a+b)(a−b)a−b=x+y+z−a−b.