Evaluate- a3 - b3 - c3 - 3abc-a2 - b2 - c2 - ab - bc - ca

The correct option is B a + b + c a ^ 3 + b ^ 3 + c ^ 3 3abc a ^ 2 + b ^ 2 + c ^ 2 ab bc ca =( a+b+c ) ( a ^ 2 + b ^ 2 + c ^ 2 ab bc ca ) ...

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(a + b)^2 Expansion and Visualisation

Evaluate: a...

Question

Evaluate: $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a}$

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a + b + c

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Solution

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\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a b + b c + c a - a^{2} - b^{2} - c^{2}}

a = - 5, b = - 6, c = 10

a + b + C = 12

a^{2} + b^{2} + c^{2} = 50

a b + b c + a c

a^{3} + b^{3} + c^{3} - 3 a b c

\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a b + b c + c a - a^{2} - b^{2} - c^{2}}

a = - 5, b = - 6, c = 10

\frac{x^{3} + y^{3} + z^{3} - 3 x y z}{a^{3} + b^{3} + c^{3} - 3 a b c} \times \frac{a^{2} + b^{2} + c^{2} - a b - b c - c a}{x^{2} + y^{2} + z^{2} - x y - y z - z x}

a^{3} + b^{3} + c^{3} - 3 a b c = \frac{1}{2} (a + b + c) [(a - b)^{2} + (b - c)^{2} + (c - a)^{2}]

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