1: \(=\left(a+b-c-a+b\right)\left(a+b-c+a-b\right)-2ab+2bc\)
\(=\left(2b-c\right)\left(2a-c\right)-2ab+2bc\)
\(=4ab-2bc-2ac+c^2-2ab+2bc\)
\(=2ab-2ac+c^2\)
2:
Đặt \(C=\left(a+b+c\right)^2+\left(b+c-a\right)^2+\left(c+a-b\right)^2+\left(a+b-c\right)^2\)
\(A=\left(a+b+c\right)^2+\left(a+b-c\right)^2\)
\(=\left(a+b\right)^2+2c\left(a+b\right)+c^2+\left(a+b\right)^2-2c\left(a+b\right)+c^2\)
\(=2\left(a+b\right)^2+2c^2\)
\(B=\left(b+c-a\right)^2+\left(c+a-b\right)^2\)
\(=\left(a-b-c\right)^2+\left(a-b+c\right)^2\)
\(=2\left(a-b\right)^2+c^2\)
\(C=2\left(a-b\right)^2+2\left(a+b\right)^2+2c^2\)
\(=2\left(2a^2+2b^2\right)+2c^2\)
\(=4a^2+4b^2+2c^2\)
