$x^3{y}^3-<!--\; -\; -->c^3=(xy{)}^3-<!--\; -\; -->c^3=(xy-<!--\; -\; -->c)((xy{)}^2+xyc+c^2)=(xy-<!--\; -\; -->c)(x^2{y}^2+xyc+c^2)$

$m^6{n}^3+p^{12}=(m^{2}n{)}^3+(p^4{)}^3=(m^{2}n+p^4)((m^{2}n{)}^2-<!--\; -\; -->m^{2}n{p}^4+(p^4{)}^2)=(m^{2}n+p^4)(m^4{n}^2-<!--\; -\; -->m^{2}n{p}^4+p^8)$

$a^3+m^3{n}^9=(a^3+(m{n}^3{)}^3)=(a+m{n}^3)(a^2-<!--\; -\; -->am{n}^3+(m{n}^3{)}^2)=(a+m{n}^3)(a^2-<!--\; -\; -->am{n}^3+m^2{n}^6)$

$q^3-<!--\; -\; -->c^{15}{d}^{18}=q^3-<!--\; -\; -->(c^5{d}^6{)}^3=(q-<!--\; -\; -->c^5{d}^6)(q^2+q{c}^5{d}^6+(c^5{d}^6{)}^2)=(q-<!--\; -\; -->c^5{d}^6)(q^2+q{c}^5{d}^6+c^{10}{d}^{12})$