Question

分解因式：x^2-(m^2+n^2)x+mn(m^2-n^2)

Answer 1

x^2-(m^2+n^2)x+mn(m^2-n^2)

=【x ﹣ m(m－n)】【x﹣ n(m＋n)】
=（x－m²＋mn）（x－n²－mn）

十字相乘

x ﹣ m(m－n)

×

x ﹣n(m＋n)

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Answer 2

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)