Multiplying a trinomial by a binomial

Multiplying a trinomial by a binomial is a lot like multiplying a binomial by a binomial. You multiply the first term by all the factors of the second term, then multiply the outer(last) term by all the factors of the second term, then simplify.

Consider the example:

(x+5) (5x² + 3x + 6)

First we multiply our first term (x) by every term in the trinomial (5x² + 3x + 6)

this gives us:

(5x³ + 3x² + 6x)

next we multiply our outer term (5) by every term in the trinomial (5x² + 3x + 6)

this gives us:
(25x² + 15x + 30)

so we have
(5x³ + 3x² + 6x) + (25x² + 15x + 30)

we can simplify by adding like terms to get:
(5x³ + 28x² + 21x + 30)