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

Prove that : |{:(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}| .

Prove that |{:(b+c, c+a, a+b),(c+a, a+b,b+c),(a+b, b+c, c+a):}| =2(a+b+c)(ab+bc+ca-a^(2)-b^(2)-c^(2)).

Show that ,,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]|=2(a+b+c)^(3)

Show that ,,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]|=2(a+b+c)^(3)

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))

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

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

Using properties of determinants 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 : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Prove that : |{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)