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Prove that : {(vec(b)+vec(c ))xx(vec...

Prove that :
`{(vec(b)+vec(c ))xx(vec(c )+vec(a))}.(vec(a)+vec(b))=2[vec(a)vec(b)vec(c )]`

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Prove that: [vec(a)" "vec(b)" "vec( c )+vec(d)]=[vec(a)" "vec(b)" "vec( c )]+[vec(a)" "vec(b)" "vec(d)] .

[(vec(a) xx vec(b)) xx (vec(b) xx vec(c)), (vec(b) xx vec(c)) xx (vec(c) xx vec(a)),(vec(c) xx vec(a)) xx (vec(a) xx vec(b))] is equal to