# Question Video: Simplifying an Algebraic Expression by Multiplying Monomials by Binomials Mathematics • 9th Grade

Simplify the expression 2π₯(π₯π¦ + π¦) β π¦(2π₯ β π¦) β π₯Β²(2π¦ β 1).

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### 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, weβll have to do some distribution. So letβs start here. We need to distribute this multiplication across both terms in the parentheses. That means weβre multiplying two π₯ times π₯π¦. And then weβll be adding two π₯ times π¦. Now, for our second set of parentheses, weβll need to be a bit more careful because weβre multiplying by negative π¦. And that means weβll have negative π¦ times two π₯.

We want to write this as plus negative π¦ times two π₯. And then weβll multiply negative π¦ by negative π¦. So weβll 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 weβre multiplying. And weβll 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 Iβve put here is kind of an intermediate step. Once you get really good at these type of problems, you wonβt 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¦ doesnβt have to be like this, but itβs 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.

Weβve 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.