\[x^{2}-y^{2}=(x-y)(x+y)\]
\[x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})\]
\[x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})\]
\[x^{4}-y^{4}=(x-y)(x+y)(x^{2}+y^{2})\]
\[x^{5}-y^{5}=(x-y)(x^{4}+x^{3}y+x^{2}y^{2}+xy^{3}+y^{4})\]
\[x^{5}+y^{5}=(x+y)(x^{4}-x^{3}y+x^{2}y^{2}-xy^{3}+y^{4})\]