PTĐTTNT:\(3abc+a^2\left(a-b-c\right)+b^2\left(b-a-c\right)+c^2\left(c-b-a\right)-c\left(b-c\right)\left(a-c\right)\)
\(=3abc+a^3-a^2b-a^2c+b^3-b^2a-b^2c+c^3-c^2b-c^2a-\left(abc-bc^2-c^2a+c^3\right)\)
\(=2abc+a^3-a^2b-a^2c+b^3-b^2c-b^2a\)
\(=\left(a^3+a^2b-a^2c\right)-\left(2a^2b+2ab^2-2abc\right)+\left(ab^2+b^3-b^2c\right)\)
\(=a^2\left(a+b-c\right)-2ab\left(a+b-c\right)+b^2\left(a+b-c\right)\)
\(=\left(a+b-c\right)\left(a^2-2ab+b^2\right)\)
\(=\left(a+b-c\right)\left(a^2-2ab+b^2\right)\)
\(=\left(a+b-c\right)\left(a-b\right)^2\) nha !
P/S:Ko có mục đích xấu,đăng lên cho bạn thôi.
Giỏi quá à :3