In this video, we are going to look at how to multiply a binomial by a trinomial. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

For example:
To multiply $(x+6)(x^2+4x-5)$ we have to distribute each term in the binomial to each term in the trinomial.
When we distribute the x to the terms in the trinomial, we get $x^3$, $4x^2$, and$-5x$. When we distribute the 6 to the trinomial, we get $6x^2$,$24x$, and $-30$. So now we are left with
$x^3+4x^2-5x+6x^2+24x-30$
From here, we want to combine like terms, to give us a final answer of
$x^3+10x^2+16x-30$

## Video-Lesson Transcript

Let’s go over multiplying a binomial by a trinomial.

It’s a two-term expression times a three-term expression.

For example:

$(x + 6) (x^2 + 4x - 5)$

Similar in multiplying a binomial by a binomial, we have to distribute each term on the first expression into each term of the second expression.

$x^3 + 4x^2 - 5x + 6x^2 + 24x - 30$ $x^3 + 10x^2 + 19x - 30$

The answer would still be the same even if we write the expressions like this:

$(x^2 + 4x - 5) (x + 6)$
$x^3 + 6x^2 + 4x^2 + 24x - 5x - 30$

If you take a closer look, this is the same as our answer above, they are just in different order.

So when we combine like terms, our answer is

$x^3 + 10x^2 + 19x - 30$

Both cases will give us the same answer.