因式分解36m^2n^2-(9m^2+n^2)^2

1个回答

  • 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