### Video Transcript

Simplify the expression two π₯
times π₯π¦ plus π¦ minus π¦ times two π₯ minus π¦ minus π₯ squared times two π¦
minus one.

First, we copy down our
expression. In this expression, everywhere we
see parentheses, weβll have to do some distribution. So letβs start here. We need to distribute this
multiplication across both terms in the parentheses. That means weβre multiplying two π₯
times π₯π¦. And then weβll be adding two π₯
times π¦. Now, for our second set of
parentheses, weβll need to be a bit more careful because weβre multiplying by
negative π¦. And that means weβll have negative
π¦ times two π₯.

We want to write this as plus
negative π¦ times two π₯. And then weβll multiply negative π¦
by negative π¦. So weβll write that as plus
negative π¦ times negative π¦. And when we come to the third set,
we see the same thing. We have a negative π₯ squared weβre
multiplying. And weβll write that as plus
negative π₯ squared times two π¦ and then negative π₯ squared times negative one,
which we write as plus negative π₯ squared times negative one.

This step that Iβve put here is
kind of an intermediate step. Once you get really good at these
type of problems, you wonβt have to write this out all the way. Instead, you would just say two π₯
times π₯π¦ equals two π₯ squared π¦ and two π₯ times π¦ is two π₯π¦. Negative π¦ times two π₯ we would
rewrite as negative two π₯π¦. This is because we generally list
the coefficient first. And the order of π₯ and π¦ doesnβt
have to be like this, but itβs good to keep that consistent throughout the same
expression. From there, negative π¦ times
negative π¦ is positive π¦ squared. And negative π₯ squared times two
π¦ we would write as negative two π₯ squared π¦. And finally, negative π₯ squared
times negative one we write as positive π₯ squared.

Weβve done all of our expanding and
multiplying, but our instructions tell us to simplify. When we look at the term two π₯
squared π¦, we also see another like term negative two π₯ squared π¦. And when we add these two values
together they equal zero. We also recognize we have the term
two π₯π¦ and negative two π₯π¦. When we add those together, we get
zero, which means our remaining values are π¦ squared and π₯ squared. So we could write the simplified
form of this expression as π₯ squared plus π¦ squared.