Using properties of determinants, prove that:` |[b^2+c^2,a^2,a^2],[b^2,c^2+a^2,b^2],[c^2,c^2,a^2+b^2]|=4a^2b^2c^2`

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^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)

Using properties of determinants,prove that det[[-a^(2),ab,acba,-b^(2),bcca,cb,-c^(2)]]=4a^(2)b^(2)c^(2)

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

Using properties of determinants,prove that: (a+b)^(2),ca,cbca,(c+b)^(2),abcb,ab,(c+a)^(2)]]=2abc(a+b+c)^(3)

Using the properties of determinants,prove that ollowing det[[a-b,-c^(2),a^(2)a^(2),-c,-a^(2)b^(2),c^(2),-a-b]]=(a+b+c)^(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: ,,(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 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)

Prove 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)