Hey, this is my first post so if this is posted in the wrong place just tell me.

Let A and B be convex sets in R^{n}. Show that [A ∪ B] = {sa + tb: a ∈ A, b ∈ B, s,t ∈ R, s + t = 1}

I already showed that {sa + tb: a ∈ A, b ∈ B, s,t ∈ R, s + t = 1} ⊆ [A ∪ B]. Also clearly A ∪ B ⊆{sa + tb: a ∈ A, b ∈ B, s,t ∈ R, s + t = 1}. So I just need to show that the given set is convex, which is what I'm having trouble with.