Question

Viết BT sau dưới dạng tổng 3 bình phương :

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

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

Answer 1

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

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

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

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

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

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

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

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

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