Xavier said the product of a monomial and a binomial will always be a trinomial. Explain the error in his reasoning.

See below.

Step-by-step explanation:

Each term in the binomial (there are 2 terms, by definition) is multiplied by the single term (monomial) so the answer will be another binomial.

For example:

2x (x - 6)

= 2x^2 - 12x.

All that is needed is a single counter-example.

One counter-example is to multiply the monomial x^3 with the binomial x^7-10x^4

We then get ...

x^3 * (x^7-10x^4) = x^3*x^7 + x^3 * (-10x^4)

x^3 * (x^7-10x^4) = x^10 - x^7

The result we get is a binomial as there are still only two terms here. We would need three terms to have a trinomial.