( a^2 – b^2 ) /( a – b ) = a + b
( a^3 – b^3 ) /( a – b ) = [( a – b )*( a^2 + b^2 ) – ab*( a – b )]
= a^2 + ab + b^2
( a^4 – b^4 ) /( a – b ) = ( a^2 + b^2 ) * ( a^2 – b^2 )
= ( a^2 + b^2 ) * ( a + b )
= a^3 + a^2b + ab^2 + b^3
规律:( a^n – b^n )/( a – b ) 由 n 个a^mb^l项构成,
其中,m = (n-1),(n-2),...0,m + l =( n - 1),即:l = n - 1 - m,由此得出结论:
( a^n – b^n ) /( a – b ) = a^( n – 1 ) + a^(n – 2)b + … + ab^( n – 2 ) + b^( n – 1 )