因式分解2m^2012 (m-n)^2 -3m^2011 n(n^2-m^2)

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因式分解2m^2012 (m-n)^2 -3m^2011 n(n^2-m^2)

因式分解2m^2012 (m-n)^2 -3m^2011 n(n^2-m^2)
因式分解2m^2012 (m-n)^2 -3m^2011 n(n^2-m^2)

因式分解2m^2012 (m-n)^2 -3m^2011 n(n^2-m^2)
2m^2012·( m - n )² - 3m^2011·n( n² - m² )
= 2m^2012 ( m - n )² + 3m^2011·n( m² - n² )
= 2m^2012 ( m - n )² + 3m^2011·n( m + n )( m - n )
= m^2011·( m - n )[ 2m( m - n ) + 3n( m + n ) ]
= m^2011·( m - n )( 2m² + mn + 3n² )

2m^2012 (m - n)" - 3m^2011 n (n" - m")
= 2m (m^2011) (m - n)" + 3n (m^2011) (m" - n")
= (m^2011) [ 2m (m - n)" + 3n (m - n)(m + n) ]
= (m^2011) (m - n)[ 2m (m - n) + 3n (m + n) ]
= (m^2011) (m - n)[ 2m" - 2mn + 3mn + 3n" ]
= (m^2011) (m - n) (2m" + mn + 3n")