Factorise `ab(a^2+b^2-c^2)-bc(c^2-a^2-b^2)+ca(a^2+b^2-c^2)`

Factorise a^(2)-2ab+b^(2)-c^(2)c^(2)

Show that |abca^(2)b^(2)c^(2)baab|=|111a^(2)b^(2)c^(2)a^(2)b^(2)c^(3)|=(a-b)(b-c)(c-a)(ab+bc+ca)

If ab+bc+ca=0 , then the value of ((b^(2)-ca)(c^(2)-ab)+(a^(2)-bc)(c^(2)-ab)+(a^(2)-bc)(b^(2)-ca))/((a^(2)-bc)(b^(2)-ca)(c^(2)-ab)) is

det[[bc-a^(2),ca-b^(2),ab-c^(2)ca-b^(2),ab-c^(2),bc-a^(2)ab-c^(2),bc-a^(2),ca-b^(2)]]=det[[a,b,cb,c,ac,a,b]]^(2)

Find the product of (a+b+2c)(a^2+b^2+4c^2 -ab-2bc-2ca) . (a+b+2c)(a^2+b^2+4c^2 -ab-2bc-2ca) का गुणनफल ज्ञात करें ।

If a, b and c are distinct positive real numbers such that Delta_(1) = |(a,b,c),(b,c,a),(c,a,b)| and Delta_(2) = |(bc - a^2, ac -b^2, ab - c^2),(ac - b^2, ab - c^2, bc -a^2),(ab -c^2, bc - a^2, ac - b^2)| , then

The determinant |(a^2,a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b)^2,ab)| is divisible by

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