By using properties of determinants. Show that: (i) `|a-b-c2a2a2bb-c-a2b2c2cc-a-b|=(a+b+c)^3` (ii) `|x+y+2z x y z y+z+2x y z x z+x+2y|=2(x+y+z)^3`

By using properties of determinants. Show that: (i) |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3 (ii) |[x+y+2z, x, y],[ z, y+z+2x, y],[ z, x, z+x+2y]|=2(x+y+z)^3

By using properties of determinants , show that : (i) {:|( a-b-c, 2a, 2a),( 2b, b-c-a, 2b ) , ( 2c,2c, c-a-b) |:} = ( a+b+c)^(3) (ii) {:|( x+y+2z, x,y ),( z, y+z+2x, y ),( z,x,z+x+2y )|:} =2( x+y+z)^(3)

Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3 or |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

Show that |a b c a+2x b+2y c+2z x y z|=0

Show that |a b c a+2x b+2y c+2z x y z|=0

Show that |{:(x,y,z),(2x+2a,2y+2b,2z+2c),(a,b,c):}|=0

Show that |{:(x,y,z),(2x+2a,2y+2b,2z+2c),(a,b,c):}|=0

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)