Đơn giản, phân tích thành nhân tử: $(x-y)^2(y-z)^2+(y-z)^2(z-x)^2+(z-x)^2(x-y)^2$

0 bình luận về “Đơn giản, phân tích thành nhân tử: $(x-y)^2(y-z)^2+(y-z)^2(z-x)^2+(z-x)^2(x-y)^2$”

1. Đáp án:

    

   Giải thích các bước giải:

   `(x−y)^2(y−z)^2+(y−z)^2(z−x)^2+(z−x)^2(x−y)^2`
   `=[(x−y)(y−z)]^2+[(y−z)(z−x)]^2+[(z−x)(x−y)]^2+2(x−y)(y−z)(z−x)(x−y)+(y−z)(z−x)(x−y)(y−z)+(z−x)(x−y)(y−z)(z−x)−2(x−y)(y−z)(z−x)(x−y)+(y−z)(z−x)(x−y)(y−z)+(z−x)(x−y)(y−z)(z−x)`
   `=[(x−y)(y−z)+(y−z)(z−x)+(z−x)(x−y)]^2−2(x−y)(y−z)(z−x)(x−y+y−z+z−x)`
   `=[(x−y)(y−z)+(y−z)(z−x)+(z−x)(x−y)]^2-0`
   `=[(x−y)(y−z)+(y−z)(z−x)+(z−x)(x−y)]^2`
   `=(xy-xz-y^2+yz+yz-xy-z^2+zx+zx-zy-x^2+xy)^2`
   `=(xy+yz+zx-x^2-y^2-z^2)^2`

   Bình luận

2. $(x-y)^2(y-z)^2+(y-z)^2(z-x)^2+(z-x)^2(x-y)^2$
   $={[(x-y)(y-z)]^2+[(y-z)(z-x)]^2+[(z-x)(x-y)]^2+2(x-y)(y-z)(z-x)(x-y)+(y-z)(z-x)(x-y)(y-z)+(z-x)(x-y)(y-z)(z-x)}-2(x-y)(y-z)(z-x)(x-y)+(y-z)(z-x)(x-y)(y-z)+(z-x)(x-y)(y-z)(z-x)$

   $=[(x-y)(y-z)+(y-z)(z-x)+(z-x)(x-y)]^2-2(x-y)(y-z)(z-x)(x-y+y-z+z-x)$
   $=[(x-y)(y-z)+(y-z)(z-x)+(z-x)(x-y)]^2$

   $=(x^2+y^2+z^2-xy-yz-xz)^2$

    

   Bình luận