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(???)²ときたら文字に置き換える率がそこそこ高い

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何番でしょうか。6問も一度にじゃ辛いですので、とりあえず

(6)

 a²-b²+2b-1

=a²-(b²-2b+1)

=a²-(b-1)²

=a²-M²

={a+M}{a-M}

={a+(b-1)}{a-(b-1)}

={a+b-1}{a-b+1}

=(a+b-1)(a-b+1)

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Were you able to resolve your confusion?