$e,(x+y)^5-x^5+y^5=5x^4y+10x^3y^2+10x^2y^3+5xy^4=5xy(x^3+2x^2y+2xy^2+1)=5xy(x^3+x^2y+xy^2+x^2y+xy^2+y^3)=5xy(x+y)(x^2+xy+y^2)$
$e,(x+y)^5-x^5
-y^5=5x^4y+10x^3y^2+10x^2y^3+5xy^4=5xy(x^3+2x^2y+2xy^2+1)=5xy(x^3+x^2y+xy^2+x^2y+xy^2+y^3)=5xy(x+y)(x^2+xy+y^2)$