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[8,b+c,a^(2)],[b,c+a,b^(2)],[c,a+b,c^(2)...

[8,b+c,a^(2)],[b,c+a,b^(2)],[c,a+b,c^(2)]|

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Prove that |(a,b+c,a^(2)),(b,c+a,b^(2)),(c,a+b,c^(2))|=-(a+b+c)xx(a-b)(b-c)(c-a).

Prove that det[[a,b+c,a^(2)b,c+a,b^(2)c,a+b,c^(2)]]=-(a+b+c)xx(a-b)(b-c)(c-a)

Show that |(b+c,a,a^(2)),(c+a,b,b^(2)),(a+b,c,c^(2))|=(a+b+c)(a-b)(b-c)(c-a)

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

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

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

[[a,a^(2),(b+c)b,b^(2),(a+c)c,c^(2),(a+b)]]=(b-c)(c-a)(a-b)(a+b+c)

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

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

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