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

Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(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)

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

det[[ Show that a,b-c,c+ba+c,b,c-aa-b,b+a,c]]=(a+b+c)(a^(2)+b^(2)+c^(2))

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

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

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

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

Using properties of determinants, prove that |[a,b,c] , [a^2,b^2,c^2] , [b+c,c+a,a+b]|=(a+b+c)(a-b)(b-c)(c-a)

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