Question

Rút gọn các biểu thức 

a) (a+b-c)² +(a-b+c)² -2(b-c)²

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

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

Giúp mình vs nha mí bạn

Answer 1

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

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

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

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

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

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

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

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