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It is shown in this paper (Theorem 1) that if α and β are real numbers such that α gb is irrational and algebraic, then there exist two (necessarily distinct) distributions S and T on R, both with compact supports, such that δ′ = ΔαS + ΔβT. Here ΔαS means S − Sα and Sα denotes the translate of S by α. It is also shown that δ′ has no such representation if α gb has rational or certain transcendental values, and that S and T can be chosen to have order two and no lower order. If ϑ belongs to any of the spaces D, E, S or their duals then ϑ ∗ S and ϑ ∗ T belong to the same space as ϑ, and ϑ′ = Δ α (ϑ ∗ S) + Δ β (ϑ ∗ T) . The formula δ′ = ΔαS + ΔβT is generalized to Rn by means of the tensor product of distributions, and it follows from this formula that there is no discontinuous translation-invariant linear form on any of the spaces D (Rn), E (Rn), S (Rn) or their duals. The same thing is also proved for E (Tn) and its dual where Tn denotes the n-dimensional torus group.