1)
<=> (x−y−z)(x−y−z)
<=> x(x−y−z)−y(x−y−z)−z(x−y−z)
<=>x^2−xy−xz−y(x−y−z)−z(x−y−z)
<=>x^2−xy−xz−(yx−y2−yz)−z(x−y−z)
<=>x^2−xy−xz−(yx−y^2−yz)−(zx−zy−z^2)
<=>x^2−xy−xz−yx+y^2+yz−zx+zy+z^2
<=>x^2+(−xy−xy)+(−xz−xz)+y^2+(yz+yz)+z^2
<=>x^2+y^2+z^2-2xy+2yz−2xz
2)
<=>(x+y−z)(x+y−z)
<=>x(x+y−z)+y(x+y−z)−z(x+y−z)
<=>x^2+xy−xz+y(x+y−z)−z(x+y−z)
<=>x^2+xy−xz+yx+y^2−yz−z(x+y−z)
<=>x^2+xy−xz+yx+y^2−yz−(zx+zy−z^2)
<=>x^2+xy−xz+yx+y^2−yz−zx−zy+z^2
<=>x^2+(xy+xy)+(−xz−xz)+y^2+(−yz−yz)+z^2
<=>x^2+y^2+z^2+2xy−2yz−2xz
3)
<=>x(x^3+x^2y+xy^2+y^3)−y(x^3+x^2y+xy^2+y^3)
<=>x^4+x^3y+x^2y^2+xy^3−y(x^3+x^2y+xy^2+y^3)
<=>x^4+x^3y+x^2y^2+xy^3−(yx^3+y^2x^2+y^3x+y^4)
<=>x^4+x^3y+x^2y^2+xy^3−yx^3−y^2x^2−y^3x−y^4
<=>x^4+(x^3y−x^3y)+(x^2y^2−x^2y^2)+(xy^3−xy^3)−y4
<=>x4−y4
4)
<=>x(x^4−x^3y+x^2y^2−xy^3+y^4)+y(x^4−x^3y+x^2y^2−xy^3+y^4)
<=>x^5−x^4y+x^3y^2−x^2y^3+xy^4+y(x^4−x^3y+x^2y^2−xy^3+y^4)
<=>x^5−x^4y+x^3y^2−x^2y^3+xy^4+yx^4−y^2x^3+y^3x^2−y^4x+y^5
<=>x^5+(−x^4y+x^4y)+(x^3y^2−x^3y^2)+(−x^2y^3+x^2y^3)+(xy^4−xy^4)+y^5
<=>x^5+y^5
#Tks
