Toán Lớp 8: ( x-y+6)(x+y-6) (y+2z-3)(y-2z-3) (x+2y-3z)(2y+3z-x)

Question

Toán Lớp 8:  ( x-y+6)(x+y-6) (y+2z-3)(y-2z-3) (x+2y-3z)(2y+3z-x)

ankim · Answer

***Lời giải***    ( x-y+6)(x+y-6)     =x(x+y-6)-y(x+y-6)+6(x+y-6)     =x^2+xy-6x-xy-y^2+6y+6x+6y-36     =x^2-y^2+(xy-xy)+(-6x+6x)+(6y+6y)-36     =x^2-y^2+12y-36     (y+2z-3)(y-2z-3)     =y(y-2z-3)+2z(y-2z-3)-3(y-2z-3)     =y^2-2yz-3y+2yz-4z^2-6z-3y+6z+9     =y^2-4z^2+(2yz-2yz)+(6z-6z)+(-3y-3y)+9     =y^2-4z^2-6y+9     (x+2y-3z)(2y+3z-x)     =x(2y+3z-x)+2y(2y+3z-x)-3z(2y+3z-x)     =2xy+3xz-x^2+4y^2+6yz-2xy-6zy-9z^2+3xz     =-x^2+4y^2-9z^2+(6yz-6zy)+(2xy-2xy)+(3xz+3xz)     =-x^2+4y^2-9z^2+6xz

dongoclandiem · Answer

Giải đáp:     *** Ph&acirc;n t&iacute;ch th&agrave;nh hiệu hai b&igrave;nh phương:   (x-y+6).(x+y-6)   =[x-(y-6)].[x+(y-6)]   =x^2-(y-6)^2    text()   (y+2z-3).(y-2z-3)   =[(y-3)+2z].[(y-3)-2z]   =(y-3)^2-(2z)^2    text()   (x+2y-3z).(2y+3z-x)   =[2y-(3z-x)].[2y+(3z-x)]   =(2y)^2-(3z-x)^2   __________________________   ***Nếu đề l&agrave; khai triển:   (x-y+6).(x+y-6)=[x-(y-6)].[x+(y-6)]   =x^2-(y-6)^2   =x^2-(y^2-12y+36)   =x^2-y^2+12y-36    text( )   (y+2z-3).(y-2z-3)=[(y-3)+2z].[(y-3)-2z]   =(y-3)^2-(2z)^2   =y^2-6x+9-4z^2    text( )   (x+2y-3z).(2y+3z-x)=[2y-(3z-x)].[2y+(3z-x)]   =(2y)^2-(3z-x)^2   =4y^2-(9z^2-6xz+x^2)   =4y^2-9z^2+6xz-x^2   ________________________________   ***AD : (a-b).(a+b)=a^2-b^2   (a-b)^2=a^2-2ab+b^2