Question

rút gọn

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

Answer 1

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

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

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

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

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

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

\(=a.2a\)

\(=2a^2\)