计算:(m+n)(m-n)[mn-(m+n)²][(m-n)²+mn]
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2014-05-21
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(m+n)(m-n)[mn-(m+n)²][(m-n)²+mn]
=(m+n)(m-n)[mn-(m²+2mn+n²)(m²-2mn+n²+mn)
=-(m+n)(m²-mn+n²)(m-n)(m²+mn+n²)
=-(m³+n³)(m³-n³)
=-(m^6-n^6)
=n^6-m^6
=(m+n)(m-n)[mn-(m²+2mn+n²)(m²-2mn+n²+mn)
=-(m+n)(m²-mn+n²)(m-n)(m²+mn+n²)
=-(m³+n³)(m³-n³)
=-(m^6-n^6)
=n^6-m^6
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