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Multiplying a Binomial by a Trinomial

In this video, we are going to look at how to multiply a binomial by a trinomial.

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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

Then combine like terms

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.