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`

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)

Prove that |((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+z)(c+z),(c+z)(a+z),(a+z)(b+z))|=(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)dot

Prove that |{:((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+z)(c+z),, (c+z)(a+z),,(a+z)(b+x)):}| = (b-c) (c-a) (a-b) (y-z) (z-x) (x-y)

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|= 2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|=2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

prove that, |{:(x,b,c),(a,y,c),(a,b,z):}|=(x-a)(y-b)(z-c)((x)/(x-a)+(y)/(y-b)+(z)/(z-c)-2)

If (a)/(x-a) + (b)/(y-b) + (c )/(z-c)=2 find (x)/(x-a) + (y)/(y-b) + (z)/(z-c) = ?

If (x)/(b+c-a)=(y)/(c+a-b)=(z)/(a+b-c) show that (b-c)x+(c-a)y+(a-b)z=0