因式分解【ab-1】的平方+【a+b-2】乘【a+b-2ab】
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因式分解【ab-1】的平方+【a+b-2】乘【a+b-2ab】
![因式分解【ab-1】的平方+【a+b-2】乘【a+b-2ab】](/uploads/image/z/12421764-36-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E3%80%90ab-1%E3%80%91%E7%9A%84%E5%B9%B3%E6%96%B9%2B%E3%80%90a%2Bb-2%E3%80%91%E4%B9%98%E3%80%90a%2Bb-2ab%E3%80%91)
(ab-1)^2+(a+b-2ab)(a+b-2)
=(ab-1)^2+(a+b)^2-2(ab+1)(a+b)+4ab
=a^2b^2-2ab+1+4ab+(a+b)^2-2(ab+1)(a+b)
=a^2b^2+2ab+1+(a+b)^2-2(ab+1)(a+b)
=(ab+1)^2+(a+b)^2-2(ab+1)(a+b)
=(ab+1)^2-2(ab+1)(a+b)+(a+b)^2
=[(ab+1)-(a+b)]^2
=(ab+1-a-b)^2
=(ab-1)^2+(a+b)^2-2(ab+1)(a+b)+4ab
=a^2b^2-2ab+1+4ab+(a+b)^2-2(ab+1)(a+b)
=a^2b^2+2ab+1+(a+b)^2-2(ab+1)(a+b)
=(ab+1)^2+(a+b)^2-2(ab+1)(a+b)
=(ab+1)^2-2(ab+1)(a+b)+(a+b)^2
=[(ab+1)-(a+b)]^2
=(ab+1-a-b)^2