Bài tập 1:

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

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

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

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

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

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

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

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

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

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

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

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