36m^2n^2-(9m^2+n^2)^2因式分解

来源：百度知道 编辑：UC知道 时间：2024/09/28 13:34:18

原式=(6mn)^2-(9m^2+n^2)^2
=(6mn+9m^2+n^2)(6mn-9m^2-n^2)
=-(9m^2+6mn+n^2)(9m^2-6mn+n^2)
=-(3m+n)^2(3m-n)^2

36m^2n^2-(9m^2+n^2)^2
=36m^2n^2-81m^4-18m^2n^2-n^4
=-81m^4+18m^2n^2-n^4
=-(81m^4-18m^2n^2+n^4)
=-(9m^2-n^2)^2

=(6mn+9m^2+n^2)(6mn-9m^2-n^2)
=-(3m+n)^2(3m-n)^2

36m^2n^2-(9m^2+n^2)^2
=(6mn+9m+n^2)[6mn-(9m^2+n^2)]
=-(3m+n)^2(3m-n)^2
=-(9m^2-n^2)^2

╮(╯▽╰)╭唉，因式分解不学，真能忘得一干二净
我现在就是

你们真强悍

36m^2n^2-(9m^2+n^2)^2
=(6mn)^2-(9m^2+n^2)^2
=[(6mn)-(9m^2+n^2)][(6mn)+(9m^2+n^2)]
=(6mn-9m^2-n^2)(6mn+9m^2+n^2)
=-(-6mn+9m^2+n^2)(6mn+9m^2+n^2)
=-(3m-n)^2(3m+n)^2