求助4m^2n^2-(m^2+n^2-x^2)^2因式分解!4m^2n^2-(m^2+n^2-x^2)^2 请问这道题的解答步骤应该是怎样的,希望高手前来指教~
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![求助4m^2n^2-(m^2+n^2-x^2)^2因式分解!4m^2n^2-(m^2+n^2-x^2)^2 请问这道题的解答步骤应该是怎样的,希望高手前来指教~](/uploads/image/z/816629-5-9.jpg?t=%E6%B1%82%E5%8A%A94m%5E2n%5E2-%28m%5E2%2Bn%5E2-x%5E2%29%5E2%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%214m%5E2n%5E2-%28m%5E2%2Bn%5E2-x%5E2%29%5E2+%E8%AF%B7%E9%97%AE%E8%BF%99%E9%81%93%E9%A2%98%E7%9A%84%E8%A7%A3%E7%AD%94%E6%AD%A5%E9%AA%A4%E5%BA%94%E8%AF%A5%E6%98%AF%E6%80%8E%E6%A0%B7%E7%9A%84%2C%E5%B8%8C%E6%9C%9B%E9%AB%98%E6%89%8B%E5%89%8D%E6%9D%A5%E6%8C%87%E6%95%99%7E)
求助4m^2n^2-(m^2+n^2-x^2)^2因式分解!4m^2n^2-(m^2+n^2-x^2)^2 请问这道题的解答步骤应该是怎样的,希望高手前来指教~
求助4m^2n^2-(m^2+n^2-x^2)^2因式分解!
4m^2n^2-(m^2+n^2-x^2)^2 请问这道题的解答步骤应该是怎样的,希望高手前来指教~
求助4m^2n^2-(m^2+n^2-x^2)^2因式分解!4m^2n^2-(m^2+n^2-x^2)^2 请问这道题的解答步骤应该是怎样的,希望高手前来指教~
原式=(2mn)^2-(m^2+n^2-x^2)^2
=-(m^2+n^2+2mn-x^2)(m^2+n^2-2mn-x^2)
=-[(m+n)^2-x^2][(m-n)^2-x^2]
=-(m+n+x)(m+n-x)(m-n+x)(m-n-x)
m^2-4n^2-4n-1
=m^2-(4n^2+4n+1)
=m^2-(2n+1)^2
=(m+2n+1)*(m-2n-1)
重复利用平方差公式
=(2mn+m^2+n^2-x^2)(2mn-m^2-n^2+x^2)
=[(m+n)^2-x^2][x^2-(m-n)^2]
=(m+n+x)(m+n-x)(x+m-n)(x-m+n)
4m^2n^2-(m^2+n^2-x^2)^2
=[2mn+(m^2+n^2-x^2)]*[2mn-(m^2+n^2-x^2)]
=[(2mn+m^2+n^2)-x^2]*[-(m^2-2mn+n^2)+x^2]
=[(m+n)^2-x^2]*[x^2-(m-n)^2]
=[(m+n+x)*(m+n-x)]*[(x+m-n)*(x-m+n)]
=(m+n+x)(m+n-x)](x+m-n)(x-m+n)
(2mn+m^2+n^2-x^2)(2mn-m^2-n^2+x^2)=<(m+n)^2-x^2>
4m^2n^2-(m^2+n^2-x^2)^2
=(2mn)^2-(m^2+n^2-x^2)^2 化简
=(2mn+m^2+n^2-x^2)(2mn-m^2-n^2+x^2) 平方差
=[(m+n)^2-x^2][-(m-n)^2+x^2] 完全平方
=(m+n+x)(m+n-x)(x+m-n)(x-m+n) 平方差
4m^2n^2-(m^2+n^2-x^2)^2
=(2mn)^2-(m^2+n^2-x^2)^2
=(2mn+m^2+n^2-x^2)(2mn-m^2-n^2+x^2)
=[(2mn+m^2+n^2)-x^2](x^2-(m^2-2mn+n^2)]
=[(m+n)^2-x^2][x^2-(m-n)^2]
=(m+n+x)(m+n-x)(x+m-n)(x-m+n)
原式等于[2mn+(m^2+n^2-x^2)]*[2mn-(m^2+n^2-x^2)]
=[(2mn+m^2+n^2)-x^2]*[-(m^2-2mn+n^2)+x^2]
=[(m+n)^2-x^2]*[x^2-(m-n)^2]
=[(m+n+x)*(m+n-x)]*[(x+m-n)*(x-m+n)]
=(m+n+x)(m+n-x)](x+m-n)(x-m+n)
4m^2n^2-(m^2+n^2-x^2)^2
=[2mn+(m^2+n^2-x^2)]*[2mn-(m^2+n^2-x^2)]
=[(2mn+m^2+n^2)-x^2]*[-(m^2-2mn+n^2)+x^2]
=[(m+n)^2-x^2]*[x^2-(m-n)^2]
=[(m+n+x)*(m+n-x)]*[(x+m-n)*(x-m+n)]
=(m+n+x)(m+n-x)](x+m-n)(x-m+n)
原式=(2mn+m^2+n^2-x^2)(2mn-m^2-n^2+x^2)
=[(m+n)^2-x^2][x^2-(m-n)^2]
=(m+n+x)(m+n-x)(x+m-n)(x-m+n)
4m^2n^2-(m^2+n^2-x^2)^2
原式=(2mn)^2-(m^2+n^2-x^2)^2
=[2mn+(m^2+n^2-x^2)]*[2mn-(m^2+n^2-x^2)]
=[(2mn+m^2+n^2)-x^2]*[-(m^2-2mn+n^2)+x^2]
=[(m+n)^2-x^2]*[x^2-(m-n)^2]
=[(m+n+x)*(m+n-x)]*[(x+m-n)*(x-m+n)]
=(m+n+x)(m+n-x)](x+m-n)(x-m+n)