作业帮因式分解,ab(a+b)^2-(a+b)^2+1首先设a+b为x,得到（ab-1)x^2+1.后面怎么办?
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因式分解,ab(a+b)^2-(a+b)^2+1首先设a+b为x,得到（ab-1)x^2+1.后面怎么办?
因式分解,
ab(a+b)^2-(a+b)^2+1
首先设a+b为x,
得到（ab-1)x^2+1.后面怎么办?
因式分解,ab(a+b)^2-(a+b)^2+1首先设a+b为x,得到（ab-1)x^2+1.后面怎么办?
能简则简吧
ab(a+b)² - (a+b)² + 1
=(ab-1)(a+b)² + 1
=(ab-1)(a²+b²+2ab) + 1
=(ab-1)(a²+b²) + 2ab(ab-1) + 1
=(ab-1)(a²+b²) + 2(ab)² - 2ab + 1
=(ab)² + (ab-1)(a²+b²) + (ab)² - 2ab + 1
=(ab-1)² + (a²+b²)(ab-1) + a²b²
把ab-1看成x,发现原式 = x² + (a²+b²)x + a²b² = (x + a²)(x + b²),代入
=(a² + ab - 1)(b² + ab - 1)
方法很多种的,看哪种适合自己
ab(a+b)²-(a+b)² +1
=(ab-1)(a+b)²+1
=(ab-1)a²+(ab-1)b²+2ab(ab-1)+1
=(ab-1)a²+(ab-1)b²+2(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(a...
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ab(a+b)²-(a+b)² +1
=(ab-1)(a+b)²+1
=(ab-1)a²+(ab-1)b²+2ab(ab-1)+1
=(ab-1)a²+(ab-1)b²+2(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(ab²-2ab+1)
=(ab-1)a²+(ab-1)b²+(ab)²+(ab-1)²
=[(ab-1)a²+(ab)²]+[(ab-1)b²+(ab-1)²]
=a²[(ab-1)+b²]+(ab-1)*[(ab-1)+b²]
=(a²+ab-1)(b²+ab-1)
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