Prove that `|a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3`

Show that: |aa+ba+b+c2a3a+2b4a+3b+2c3a6a+3b10a+6b+3c|=a^(3)

Using properties of determinants,prove that det[[a,a+b,a+b+c2a,3a+2b,4a+3b+2c3a,6a+3b,10a+6b+3c]]=a^(3)

Prove that |(a+b, b, c), (b+c, c, a), (c+a, a, b)| = 3abc - a^3-b^3-c^3.

If a=omega!=1 , is a cube root of unity b=785,c=2008i and Delta=|(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c)| then Delta equals

Prove that |b+c a-b a c+a b-c b a+b c-a c|=3a b-a^3-b^3-c^3dot

Add: 3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c

Prove that |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=- 2 (a^3+ b^3+c^3-3abc)

Prove that |[a+b,a+2b,a+3b] , [a+3b,a+4b,a+5b] , [a+5b,a+6b,a+7b]|=0

Prove that |[a,b,c] , [a^2,b^2,c^2] , [a^3,b^3,c^3]|= abc(a-b)(b-c)(c-a)

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a)(a+b+c)