binomial

in algebra, a binomial is a polynomial with two terms

the binomial $x^2-y^2$ is called difference of two squares
$x^2-y^2=(x-y)(x+y)$

this is a special case of the formula $x^{n+1}-y^{n+1}=(x-y)\sum _{k=0}^n{x}^k{y}^{n-k}$
for imaginary numbers, $x^2+y^2=x^2-(iy{)}^2=(x-iy)(x+iy)$

the product of two linear binomials is a trinomial
$(ax+b)(cx+d)=ac{x}^2+(ad+bc)x+bd$