Toán Lớp 8: Phân tích đa thức thành nhân tử: A=a.(b+c)^2.(b-c) +b(c+a) ^2.(c-a) +c(a+b) ^2.(a-b)

Question

Toán Lớp 8:  Phân tích đa thức thành nhân tử:  A=a.(b+c)^2.(b-c) +b(c+a) ^2.(c-a) +c(a+b) ^2.(a-b)

huongtructram · Answer

Giải đáp:       Lời giải và giải thích chi tiết:    a( b + c )&sup2; . ( b- c ) + b( c + a )&sup2; . ( c -a ) + c( a + b )&sup2; . ( a - b )    = a( b&sup2; + 2bc + c&sup2; )( b - c ) + b( c&sup2; + 2ac + a&sup2; )( c - a ) + c( a&sup2; + 2ab + b&sup2; )( a - b )   = ( b&sup2; + 2bc + c&sup2; )( ab - ac ) + ( c&sup2; + 2ac + a&sup2; )( bc - ab ) + ( a&sup2; + 2ab + b&sup2; )( ac - bc )   = ab&sup3; + 2ab&sup2;c + abc&sup2; - ab&sup2;c  - 2abc&sup2; - ac&sup3; + bc&sup3; + 2abc&sup2; + a&sup2;bc - abc&sup2; - 2a&sup2;bc - a&sup3;b + a&sup3;c + 2a&sup2;bc + ab&sup2;c - a&sup2;bc - 2ab&sup2;c - b&sup3;c    = ab&sup3; - ac&sup3; + bc&sup3; - a&sup3;b + a&sup3;c - b&sup3;c + ( 2ab&sup2;c - ab&sup2;c + ab&sup2;c - 2ab&sup2;c ) + ( abc&sup2; - 2abc&sup2; - abc&sup2; + 2abc&sup2; ) + ( a&sup2;bc - 2a&sup2;bc + 2a&sup2;bc - a&sup2;bc )    = ab&sup3; - ac&sup3; + bc&sup3; - a&sup3;b + a&sup3;c - b&sup3;c     = ab&sup3; - ac&sup3; + bc&sup3; - a&sup3;b + a&sup3;c - b&sup3;c  - a&sup2;bc + a&sup2;bc - ab&sup2;c + ab&sup2;c   = ( a&sup3;c + a&sup2;bc - a&sup3;b ) + ( ab&sup3; - ab&sup2;c - b&sup3;c ) - ( ac&sup3; - bc&sup3; ) - ( a&sup2;bc - ab&sup2;c )    = a&sup2;( ac + bc - ab ) + b&sup2; ( ab -ac - bc ) - c&sup3;( a - b ) - abc( a - b )   = a&sup2;( ac + bc - ab ) - b&sup2;( ac + bc - ab ) - c&sup3;( a - b ) - abc( a - b )   = ( ac + bc - ab )( a&sup2; - b&sup2; ) - c&sup3;( a - b ) - abc( a - b )   = ( ac + bc - ab )( a - b )( a + b ) - c&sup3;( a - b ) - abc( a - b )   = ( a - b )( a&sup2;c + abc - a&sup2;b + abc + b&sup2;c - ab&sup2; - c&sup3; - abc )    = ( a - b )( a&sup2;c + abc - a&sup2;b + b&sup2;c - ab&sup2; - c&sup3; )   = ( a - b ) ( a&sup2;( c - b ) + ab( c - b ) - c( c&sup2; - b&sup2; ) )    = ( a - b ) ( a&sup2;( c - b ) + ab( c - b ) - c( c - b)( c + b ) )   = ( a - b ) ( c - b ) ( a&sup2; + ab - c&sup2; - bc )   = ( a - b ) ( c - b ) ( ( a&sup2; - c&sup2; ) + b( a - c ) )    = ( a - b ) ( c - b ) ( ( a - c )( a + c ) + b( a - c ) )    = ( a - b ) ( c - b ) ( a - c ) ( a + b + c )     Ch&uacute;c bạn học  tốt v&agrave; cho mik ctlhn nh&eacute; !!!