Question

Rút gọn biểu thức:

1,(a+b-c)^2 - (a - b)^2 -2ab + 2bc

2,(a+b+c)^2 + ( b+c-a)^2 + (c+a-b)^2 + ( a+b-c)^2

Answer 1

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

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

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

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

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

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

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

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

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

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