Construction of Identities for Sums of Squares

From sum-of-squares formulas of sizes $[r,s,n]$ and $[r^{\mathrm{\prime }},s^{\mathrm{\prime }},n^{\mathrm{\prime }}]$ we construct a formula of size $[r+r^{\mathrm{\prime }},2s{s}^{\mathrm{\prime }},2n{n}^{\mathrm{\prime }}]$.