`|[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc`

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determinant (3a -a+b -a+c , -b+a 3b -b+c , -c+a -c+b 3c) = 3(a+b+c)(ab+bc+ca) determinant (3a -a+b -a+c , -b+a 3b -b+c , -c+a -c+b 3c) = 3(a+b+c)(ab+bc+ca)
If a+b+c = 16, ab+bc+ca = 78 then a^3+b^3+c^3-3abc = ? | Identity Question | Algebra If a+b+c = 16, ab+bc+ca = 78 then a^3+b^3+c^3-3abc = ? | Identity Question | Algebra
a3 + b3 + c3 - 3abc = ( a + b + c).(a2 + b2 + c2 - ab - bc - ca) a3 + b3 + c3 - 3abc = ( a + b + c).(a2 + b2 + c2 - ab - bc - ca)
prove that a³ + b³+ c³ - 3abc = ( a + b + c) ( a² + b² + c ² - ab - bc - ca ) prove that a³ + b³+ c³ - 3abc = ( a + b + c) ( a² + b² + c ² - ab - bc - ca )
If `a+b+c=6` and `ab+bc+ca=11` is given then find the value of `a^3+b^3+c^3-3abc` If `a+b+c=6` and `ab+bc+ca=11` is given then find the value of `a^3+b^3+c^3-3abc`
Prove That | a b c, a^2 b^2 c^2, a^3 b^3 c^3 |=abc(a-b)(b-c )(c-a) ||Class-12th Prove That | a b c, a^2 b^2 c^2, a^3 b^3 c^3 |=abc(a-b)(b-c )(c-a) ||Class-12th
Using the properties of determinants,prove |3a,-a+b,-a+c||a-b,3b,c-b||a-c,b-c,3c|=3(a+b+c)(ab+bc+ca) Using the properties of determinants,prove |3a,-a+b,-a+c||a-b,3b,c-b||a-c,b-c,3c|=3(a+b+c)(ab+bc+ca)
Prove that `|{:(1, 1, 1),(a, b, c),(a^(3), b^(3), c^(3)):}|=(a-b)(b-c)(c-a)(a+b+c)` Prove that `|{:(1, 1, 1),(a, b, c),(a^(3), b^(3), c^(3)):}|=(a-b)(b-c)(c-a)(a+b+c)`