Сакăр тăваткал çавахлăхĕ тесе ак çакнашкал çавахлăха калаççĕ:
( a 1 2 + a 2 2 + a 3 2 + a 4 2 + a 5 2 + a 6 2 + a 7 2 + a 8 2 ) ⋅ ( b 1 2 + b 2 2 + b 3 2 + b 4 2 + b 5 2 + b 6 2 + b 7 2 + b 8 2 ) = = ( a 1 b 1 − a 2 b 2 − a 3 b 3 − a 4 b 4 − a 5 b 5 − a 6 b 6 − a 7 b 7 − a 8 b 8 ) 2 + + ( a 2 b 1 + a 1 b 2 + a 4 b 3 − a 3 b 4 + a 6 b 5 − a 5 b 6 − a 8 b 7 + a 7 b 8 ) 2 + + ( a 3 b 1 − a 4 b 2 + a 1 b 3 + a 2 b 4 + a 7 b 5 + a 8 b 6 − a 5 b 7 − a 6 b 8 ) 2 + + ( a 4 b 1 + a 3 b 2 − a 2 b 3 + a 1 b 4 + a 8 b 5 − a 7 b 6 + a 6 b 7 − a 5 b 8 ) 2 + + ( a 5 b 1 − a 6 b 2 − a 7 b 3 − a 8 b 4 + a 1 b 5 + a 2 b 6 + a 3 b 7 + a 4 b 8 ) 2 + + ( a 6 b 1 + a 5 b 2 − a 8 b 3 + a 7 b 4 − a 2 b 5 + a 1 b 6 − a 4 b 7 + a 3 b 8 ) 2 + + ( a 7 b 1 + a 8 b 2 + a 5 b 3 − a 6 b 4 − a 3 b 5 + a 4 b 6 + a 1 b 7 − a 2 b 8 ) 2 + + ( a 8 b 1 − a 7 b 2 + a 6 b 3 + a 5 b 4 − a 4 b 5 − a 3 b 6 + a 2 b 7 + a 1 b 8 ) 2 . {\displaystyle {\begin{aligned}(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+a_{5}^{2}+a_{6}^{2}+a_{7}^{2}+a_{8}^{2})\cdot (b_{1}^{2}+b_{2}^{2}+b_{3}^{2}+b_{4}^{2}+b_{5}^{2}+b_{6}^{2}+b_{7}^{2}+b_{8}^{2})=\\=(a_{1}b_{1}-a_{2}b_{2}-a_{3}b_{3}-a_{4}b_{4}-a_{5}b_{5}-a_{6}b_{6}-a_{7}b_{7}-a_{8}b_{8})^{2}+\\+(a_{2}b_{1}+a_{1}b_{2}+a_{4}b_{3}-a_{3}b_{4}+a_{6}b_{5}-a_{5}b_{6}-a_{8}b_{7}+a_{7}b_{8})^{2}+\\+(a_{3}b_{1}-a_{4}b_{2}+a_{1}b_{3}+a_{2}b_{4}+a_{7}b_{5}+a_{8}b_{6}-a_{5}b_{7}-a_{6}b_{8})^{2}+\\+(a_{4}b_{1}+a_{3}b_{2}-a_{2}b_{3}+a_{1}b_{4}+a_{8}b_{5}-a_{7}b_{6}+a_{6}b_{7}-a_{5}b_{8})^{2}+\\+(a_{5}b_{1}-a_{6}b_{2}-a_{7}b_{3}-a_{8}b_{4}+a_{1}b_{5}+a_{2}b_{6}+a_{3}b_{7}+a_{4}b_{8})^{2}+\\+(a_{6}b_{1}+a_{5}b_{2}-a_{8}b_{3}+a_{7}b_{4}-a_{2}b_{5}+a_{1}b_{6}-a_{4}b_{7}+a_{3}b_{8})^{2}+\\+(a_{7}b_{1}+a_{8}b_{2}+a_{5}b_{3}-a_{6}b_{4}-a_{3}b_{5}+a_{4}b_{6}+a_{1}b_{7}-a_{2}b_{8})^{2}+\\+(a_{8}b_{1}-a_{7}b_{2}+a_{6}b_{3}+a_{5}b_{4}-a_{4}b_{5}-a_{3}b_{6}+a_{2}b_{7}+a_{1}b_{8})^{2}.\end{aligned}}}
