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Question

Compute the indicated products.
(i)[abba][abba]

(ii)123[2 3 4]

(iii)[1223][123231]

(iv)234345456135024305

(v)213211[101121]

(vi)[313102]231031

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Solution

[abba][abba]=[a×a+b×ba×(b)+b×a(b)×a+a×b(b)×(b)+a×a]=[a2+b2ab+abab+abb2+a2]=[a2+b200b2+a2]

1233×1[2 3 4]1×3=1×21×31×42×22×32×43×23×33×43×3=2344686912

[1223][123231]=[1×1+(2)×21×2+(2)×31×3+(2)×12×1+3×22×2+3×32×3+3×1]=[3418139]

234345456135024305=2+0+126+6+010+12+203+0+159+8+015+16+254+0+1812+10+020+20+30=140421815622270

213211[101121]=210+22+1320+43+2110+21+1=123145220

[313102]231031=[61+99+0+32+0+63+0+2]=[14645]


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