\(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c\)

\(=\left(a+b\right)^2+2.c\left(a+b\right)+c^2+\left(a+b\right)^2-2.c\left(a+b\right)+c^2-4c^2\)

\(=a^2+2ab+b^2+2ca+2cb+c^2+a^2+2ab+b^2-2ca-2cb+c^2-4c^2\)

\(=2a^2+4ab+2b^2-2c^2\)

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

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

\(=2\left(a+b+c\right)\left(a+b-c\right)\)

Mn vào tcn của con này, https://olm.vn/thanhvien/kimmai123az, PTD/KM ?, nó chuyên đi copy bài của ng khác và câu hỏi tương tự

       \(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)

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

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

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

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

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

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

Chúc bạn học tốt.

→(a+b)(a²-b²) +(b+c)(b²-a²) -(c²-a²)(b+c) +(c+a)(c²-a²)

↔(a²-b²)(a+b-b-c)-(c²-a²)(b+c-c-a)

↔(a-c)(a²-b²)-(c²-a²)(b-a)

↔(a-c)((a²-b²-(a+c)(b-a))

↔(a-c)(a-b)(a+b+b-a)

↔2b(a-c)(a-b)

\(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)

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

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

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

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

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

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

\(=\left(a-b\right)\left[a\left(b-c\right)+c\left(c-b\right)\right]\)

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

chỗ cuối phải là c^2-a^2 nha mọi người