Given a + B + C = 0, the value of the algebraic formula (a + b) (B + C) (c + a) + ABC is () A. -1B. 1C. 0D. 2

Given a + B + C = 0, the value of the algebraic formula (a + b) (B + C) (c + a) + ABC is () A. -1B. 1C. 0D. 2


∵ a + B + C = 0 ∵ a + B = - C, B + C = - A, C + a = - B ∵ (a + b) (B + C) (c + a) + ABC = - C × (- a) × (- b) + ABC = - ABC + ABC = 0



If ABC = 1, then the value of AAB + A + 1 + BBC + B + 1 + CCA + C + 1 is ()
A. 1B. 0C. -1D. -2


Then AAB + A + 1 + BBC + B + 1 + CCA + C + 1 = AC1 + AC + C + BBC + B + 1 + BC1 + BC + B = ABCB + 1 + BC + BB + B + 1 + BC1 + BC + B = 1 + B + BCB + 1 + BC = 1

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