\[(x+y)^{2}=x^{2}+2xy+y^{2}\]
\[(x-y)^{2}=x^{2}-2xy+y^{2}\]
\[(x+y)^{3}=x^{3}+3x^{2}y+3xy^{2}+y^{3}\]
\[(x-y)^{3}=x^{3}-3x^{2}y+3xy^{2}-y^{3}\]
\[(x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}\]
\[(x-y)^{4}=x^{4}-4x^{3}y+6x^{2}y^{2}-4xy^{3}+y^{4}\]
\[(x+y)^{5}=x^{5}+5x^{4}y+10x^{3}y^{2}+10x^{2}y^{3}+5xy^{4}+y^{5}\]
\[(x-y)^{5}=x^{5}-5x^{4}y+10x^{3}y^{2}-10x^{2}y^{3}+5xy^{4}-y^{5}\]