\(a^3-b^3+c^3+3abc\)
\(=a^3-3a^2b+3ab^2-b^3+c^3+3abc+3a^2b-3ab^2\)
\(=\left(a^3-3a^2b+3ab^2-b^3\right)+c^3+\left(3abc+3a^2b-3ab^2\right)\)
\(=\left(a-b\right)^3+c^3+3ab.\left(c+a-b\right)\)
\(=\left(a-b\right)^3+c^3+3ab.\left(a-b+c\right)\)
\(=\left(a-b+c\right).\left[\left(a-b\right)^2-\left(a-b\right).c+c^2\right]+3ab.\left(a-b+c\right)\)
\(=\left(a-b+c\right).\left(a^2-2ab+b^2-ac+bc+c^2\right)+3ab.\left(a-b+c\right)\)
\(=\left(a-b+c\right).\left(a^2-2ab+b^2-ac+bc+c^2+3ab\right)\)
\(=\left(a-b+c\right).\left(a^2+b^2+c^2+ab-ac+bc\right)\)
Chúc bạn học tốt!
