Show that: `|[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3`

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

Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^2, (c+a)^2, b^2],[c^2,c^2,(a+b)^2]]|= 2abc (a+b+c)^3 .

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Prove that : |[a+b+c,-c,-b],[-c, a+b+c, -a],[-b,-a,a+b+c]|= 2(a+b)(b+c)(c+a)