因式分解:x^2-(m^2+n^2)x+mn(m^2-n^2)
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因式分解:x^2-(m^2+n^2)x+mn(m^2-n^2)
![因式分解:x^2-(m^2+n^2)x+mn(m^2-n^2)](/uploads/image/z/5037964-52-4.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%3Ax%5E2-%28m%5E2%2Bn%5E2%29x%2Bmn%28m%5E2-n%5E2%29)
x^2-(m^2+n^2)x+mn(m^2-n^2)
=x^2-(m^2+n^2)x+mn(m+n)(m-n)
=x^2-(m^2+n^2)x+n(m+n)*m(m-n)
=(x-n(m+n))(x-m(m-n))
=(x-mn-n^2)(x+mn-m^2)
=x^2-(m^2+n^2)x+mn(m+n)(m-n)
=x^2-(m^2+n^2)x+n(m+n)*m(m-n)
=(x-n(m+n))(x-m(m-n))
=(x-mn-n^2)(x+mn-m^2)