Using properties of determinants prove that:


Operating C1→aC1



Operating C1→C1+bC2+cC3




Taking (a2+b2+c2) common from C1



Operating R1→R1-R3, R2→R2-R3



Operating C2→C2-C3



Taking (a+b+c) common from C2




Expanding with respect to C1




= (a2+b2+c2)(a+b+c)


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