Toán Lớp 8: x.(X+4).(x+6).(x+10)+80 Phân tích thành nhân tử

Question

Toán Lớp 8:  x.(X+4).(x+6).(x+10)+80  Phân tích thành nhân tử

mocmien87 · Answer

Giải đáp:       Lời giải và giải thích chi tiết:    x(x+4)(x+6)(x+10) + 80    = x(x+10)(x+4)(x+6) +80    =(x^2 +10x )(x^2 +4x+ 6x +24) +80    = (x^2 +10x)(x^2 +10x +24) +80  (*)    đặt t = x^2 +10x   => x^2 +10 +24 = t+24    suy ra (*) trở th&agrave;nh    t(t+24) +80    =t^2 +24t +80    = t^2 +4t +20t +80    = t(t+4) + 20(t+4)   =(t+4)(t+20)    = (x^2 +10x +4)(x^2 +10x +20 )

bichquyenlien · Answer

$ ????.(????+4).(????+6).(????+10)+80$      $ = (????+10)(????+6)????^2+4????(????+10)(????+6)+80$      $ = (????+6)????^3+10(????+6)????^2+4(????+6)????^2+40????(????+6)+80$      $ = (????+6)????^3+14(????+6)????^2+40????(????+6)+80$      $ = ????^4+6????^3+14????^3+84????^2+40????^2+240????+80$      $ = ????^4+20????^3+84????^2+40????^2+240????+80$      $ = ????^4+20????^3+124????^2+240????+80$      $ = ????^4+20????^3+124????^2+240????+80$      $ = ????^4+10????^3+20????^2+10????^3+100????^2+200????+4????^2+40????+80$      $ = (????^2+10????+20)????^2+10(????^3+10????^2+20????)+4(????^2+10????+20)$      $ = (????^2+10????+20)????^2+10????(????^2+10????+20)+4(????^2+10????+20)$      $ = (????^2+10????+4)(????^2+10????+20)$