Question

(a+b+c)^3-4(a^3+b^3+c^3) - 12abc

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Answer 1

Ta có : \(\left(a+b+c\right)^3-4\left(a^3+b^3+c^3\right)-12abc\)

\(=a^3+b^3+c^3+3\left(a+b\right)\left(a+c\right)\left(b+c\right)-4\left(a^3+b^3+c^3\right)-12abc\)

\(=-3\left(a^3+b^3+c^3\right)+3\left(a+b\right)\left(a+c\right)\left(b+c\right)-12abc\)

\(=-3\left[a^3+b^3+c^3-\left(a+b\right)\left(a+c\right)\left(b+c\right)+4abc\right]\)

\(=-3\left(a^3+b^3+c^3-c^2b-c^2a-b^2c-a^2c-ab^2-6abc\right)\)

\(=-3\left(c-b-a\right)\left(c-b+a\right)\left(c+b-a\right)\)