### Video Transcript

Expand and simplify π₯ minus two π¦
plus three times two π₯ plus π¦.

To expand the product of two
polynomials, we need to distribute one polynomial over each term in the other. So that means we could distribute
the trinomial over the binomial or the binomial over the trinomial. In this case, it seems the first
option is more straightforward. So, letβs start with distributing
the trinomial over each term in the binomial as follows. We can then expand each of the two
terms by distributing the first factor over each trinomial. For the first term, we have two π₯
times π₯ plus two π₯ times negative two π¦ plus two π₯ times three, which simplifies
to two π₯ squared minus four π₯π¦ plus six π₯. For the second term, we have π¦
times π₯ plus π¦ times negative two π¦ plus π¦ times three, which simplifies to π₯π¦
minus two π¦ squared plus three π¦.

Now we can add the expressions
together and collect like terms to simplify. We obtain two π₯ squared minus
three π₯π¦ minus two π¦ squared plus six π₯ plus three π¦. We have fully expanded and
simplified the product of π₯ minus two π¦ plus three times two π₯ plus π¦.