(x+1).(x6−x5+x4−x3+x2−x+x)
=x.x6+x.(−x5)+x.x4+x.(−x3)+x.x2+x.(−x)+x.x+1.x6+1.(−x5)+1.x4+1.(−x3)+1.x3+1.(−x)+1.x
=x7−x6+x5−x4+x3−x2+x2+x6−x5+x4−x3+x2−x+x
(x+1).(x6−x5+x4−x3+x2−x+x)(x+1).(x6−x5+x4−x3+x2−x+x)(x+1).(x6−x5+x4−x3+x2−x+x)
=x.x6+x.(−x5)+x.x4+x.(−x3)+x.x2+x.(−x)+x.x+1.x6+1.(−x5)+1.x4+1.(−x3)+1.x3+1.(−x)+1.x=x.x6+x.(−x5)+x.x4+x.(−x3)+x.x2+x.(−x)+x.x+1.x6+1.(−x5)+1.x4+1.(−x3)+1.x3+1.(−x)+1.x=x.x6+x.(−x5)+x.x4+x.(−x3)+x.x2+x.(−x)+x.x+1.x6+1.(−x5)+1.x4+1.(−x3)+1.x3+1.(−x)+1.x
=x7−x6+x5−x4+x3−x2+x2+x6−x5+x4−x3+x2−x+x=x7−x6+x5−x4+x3−x2+x2+x6−x5+x4−x3+x2−x+x=x7−x6+x5−x4+x3−x2+x2+x6−x5+x4−x3+x2−x+x
=x7
