一道初一数学计算题 因式分解

36m^2n^2-(9m^2+n^2)^2 
2025-03-10 15:22:09
推荐回答(2个)
回答1:

36m²n²-(9m²+n²)²=(6mn-9m²-n²)(6mn+9m²+n²)
=-(9m²-6mn+n²)(6mn+9m²+n²)
=-(3m-n)²(6mn+9m²+n²)
解题思路是:题目符合a²-b²=(a-b)(a+b)的形式,要把36m²n²看成a平方的形式,
即(6mn)² ;把(9m²+n²)²看成b².这是整体思想。
给你两个练习:
(1)16x²-81
(2)2ab-a²-b²+c²

回答2:

36m²n²-(9m²+n²)²=(6mn-9m²-n²)(6mn+9m²+n²)
=-(9m²-6mn+n²)(6mn+9m²+n²)
=-(3m-n)² [(3m)²+6mn+n²]
= (-3m+n)(3m-n)(3m+n)(3m+n)