Giải thích các bước giải:
a) $(x+y+z)^2$
$ = (x+y+z).(x+y+z)$
$ = x^2+xy+xz+xy+y^2+yz+zx+yz+z^2$
$ = x^2+y^2+z^2+2xy+2yz+2zx$
b) $(x+y+z)^3$
$ = (x+y+z)^2.(x+y+z)$
$= (x^2+y^2+z^2+2xy+2yz+2zx).(x+y+z)$
$ = x^3+y^3+z^3+x^2.(y+z)+y^2.(x+z)+z^2.(y+x) +(x+y+z).(2xy+2yz+2zx)$
$ = x^3+y^3+z^3 + 3.(x^2y+xy^2+y^2z+yz^2+z^2x+zx^2+2xyz)$
$ = x^3+y^3+z^3+3.[xy.(x+y) + zx.(x+y) + z^2.(x+y) + yz.(x+y)]$
$ = x^3+y^3+z^3+3.(x+y).(xy+zx+z^2+yz)$
$ = x^3+y^3+z^3+3.(x+y).[z.(y+z)+x.(y+z)]$
$ = x^3+y^3+z^3.(x+y).(y+z).(z+x)$
$ = x^3+y^3+z^3 + 3.(x+y).(y+z).(z+x)$
c) $(x^3+x^2y+xy^2+y^3).(x-y)$
$ =x^4+x^3y+x^2y^2+y^3x-x^3y-x^2y^2-xy^3-y^4$
$= x^4-y^4$
