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[" Using properties of determinant,prove that "],[[-a(b^(2)+c^(2)-a^(2)),2b',2c'],[2a',-b(c^(2)+a^(2)-b^(2)),2c'],[2a^(3),-b(c^(2)+a^(2)-b^(2)),-c(a^(2)+b^(2)-c)],[-abc(a^(2)+b^(2)+c^(2))']]

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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 properties of determinants 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 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 determinant, Show 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 determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

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 determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .