Polynomial identities involving sums and differences of like powers include x^2 - y^2 | = | (x - y)(x + y) x^3 - y^3 | = | (x - y)(x^2 + x y + y^2) x^3 + y^3 | = | (x + y)(x^2 - x y + 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 + x y^3 + y^4) x^5 + y^5 | = | (x + y)(x^4 - x^3 y + x^2 y^2 - x y^3 + y^4) x^6 - y^6 | = | (x - y)(x + y)(x^2 + x y + y^2)(x^2 - x y + y^2) x^6 + y^6 | = | (x^2 + y^2)(x^4 - x^2 y^2 + y^4), which are the polynomial versions of the so-called binomial numbers.

binomial number | Euler four-square identity | Gauss's polynomial identity | Liouville polynomial identity | perfect cubic polynomial | polynomial