Question

giup minh voi

cm a^3 +b^3 +c^3 -3*a*b*c=(a+b+c)*(a^2 +b^2 +c^2 -a*b -b*c -a*c)

Answer 1

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Answer 2

\(a^3+b^3+c^3-3abc\)

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

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

\(=\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)

\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)\)

Answer 3

phân tích vế phải ra