a, $(x-y-z)^2$
$=[(x-y)-z]^2$
$=(x-y)^2-2.(x-y).z+z^2$
$=x^2-2xy+y^2-2zx+2yz+z^2$
$=x^2+y^2+z^2-2xy+2yz-2zx$ (đpcm)
b, $(x+y-z)^2$
$=[(x+y)-z^2$
$=(x+y)^2-2(x+y).z+z^2$
$=x^2+2xy+y^2-2zx-2yz+z^2$
$=x^2+y^2+z^2+2xy-2yz-2zx$ (đpcm)
c, $(x-y)(x^3+x^2y+xy^2+y^3)$
$=x^4+x^3y+x^2y^2+xy^3-x^2y-x^2y^2-xy^3-y^4$
$=x^4-y^4$ (đpcm)
d, $(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)$
$=x^5-x^4y+x^3y^2-x^2y^3+xy^4+x^4y-x^3y^2+x^2y^3-xy^4+y^5$
$=x^5+y^5$ (đpcm)
* Nhân bung bét ra rồi rút gọn
