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,)|=(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

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

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

Using the properties of determinants, prove the following |{:(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, 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)