Prove that ` {:|( b+c,a,a), ( b,c+a,b),( c,c,b+a) |:}` = 4abc

Prove that |(b+c,a,a),(b,c+a,b),(c,c,a+b)|= 4ac

Prove that |(1,1,1),(bc,ca,ab),(b+c, c+a, a+b)| = (a-b)(b-c)(c-a)

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

Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)

|(a,b,c),(b,c,a),(c,a,b)| =

Using the property of determinants prove that {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)

Prove that |{:(,1,a,a^(2)),(,1,b,b^(2)),(,1,c,c^(2)):}|=(a-b)(b-c)(c-a)

If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) ]:}=0 Show that either a+b+c=0 "or" a= b= c .

Prove that |(1,a^2,bc),(a,b^2,ca),(1,c^2,ab)|=(a-b)(b-c)(c-a)

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}