The following is a simple example of the product of a binomial and a monomial:

(ax + b)(cx2) = acx3 + bcx2

This same principle, multiplying each term of the one polynomial by each term of the other, is directly extended to polynomials of any number of terms. For example, the product of a binomial and a trinomial is carried out as follows:

(ax3 + bx2 - cx)(dx + e) = adx4 + aex3 + bdx3 + bex2 - cdx2 - cex

After such operations have been performed, all similar terms should be combined whenever possible to simplify the entire expression:

= adx4 + (ae + bd)x3 + (be - cd)x2 - cex