Prove that `|(b+x)(c+x)(v+x)(a+x)(a+x)(b+x)(b+y)(c+y)(c+x)(a+t)(a+y)(b+y)(b+z)(c+z)(c+z)(a+z)(a+z)(b+z)|=(b-c)(c-a)(y-z)(x-y)dot`

Explanation

`|{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y),,(c+y)(a+y),,(a+y)(b+y)),((b+x)(c+z),,(c+z)(a+z),,(a+z)(b+z)):}|`
`= |{:(bc+(b+c)x+x^(2),,ac+(a+c)x+x^(2),,ab+(a+b)x+x^(2)),(bc+(b+c)y+y^(2),,ac+(a+c)y+y^(2),,ab+(a+b)y+y^(2)),(bc+(b+c)z+z^(2),,ac+(a+c)z+z^(2),,ab+(a+b)z+z^(2)):}|`
`|{:(bc,,b+c,,1),(ac,,a+c,,1),(ab,,a+b,,1):}| |{:(1,,x,,x^(2)),(1,,y,,y^(2)),(1,,z,,z^(2)):}|`
`=(b-c)(c-a)(a-b)(y-z)(z-x)(x-y)`