Consider the example:

(x+5) (5x

^{2}+ 3x + 6)

First we multiply our first term (x) by every term in the trinomial (5x

^{2}+ 3x + 6)

this gives us:

(5x

^{3}+ 3x

^{2}+ 6x)

next we multiply our outer term (5) by every term in the trinomial (5x

^{2}+ 3x + 6)

this gives us:

(25x

^{2}+ 15x + 30)

so we have

(5x

^{3}+ 3x

^{2}+ 6x) + (25x

^{2}+ 15x + 30)

we can simplify by adding like terms to get:

(5x

^{3}+ 28x

^{2}+ 21x + 30)

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