### Video Transcript

Is the equation π₯ cubed minus π¦
cubed equals π₯ minus π¦ multiplied by π₯ squared plus π₯π¦ plus π¦ squared an
identity?

So, if we look and see whether it
is an identity, we wanna see whether the left-hand side is identical to the
right-hand side. And to do that, what weβre gonna
have to do is distribute across the parentheses. And in order to distribute across
our parentheses, what weβre gonna do is multiply each of the terms in the left-hand
set by each of the terms in the right-hand set. So first to start with, π₯
multiplied by π₯ squared, which is π₯ cubed. Then, weβre gonna have π₯
multiplied by positive π₯π¦, which is gonna give us π₯ squared π¦. And then, weβre gonna have π₯
multiplied by positive π¦ squared, which is gonna give us π₯π¦ squared.

Well then, next what weβre gonna
have is negative π¦ multiplied by π₯ squared, which gives us negative π₯ squared
π¦. And then, weβre gonna have negative
π¦ multiplied by positive π₯π¦, which is gonna give us negative π₯π¦ squared. And then finally, weβve got
negative π¦ multiplied by positive π¦ squared, which is gonna give us negative π¦
cubed.

Okay, great, weβve got to this
point, but this doesnβt look like the left-hand side of our equation. But what weβre gonna have to do is
tidy up first with some simplifying. Well, first of all, weβve only got
one π₯ cubed. Well then, we have π₯ squared π¦
minus π₯ squared π¦, which means these are gonna cancel each other out because
theyβre gonna be equal to zero. So then, next weβre gonna have
positive π₯π¦ squared minus π₯π¦ squared. So again, these are gonna cancel
each other out.

And then finally, weβve got minus
π¦ cubed. So, weβre now left with π₯ cubed
minus π¦ cubed. Well, this is what we started with
on the left-hand side of the equation. So therefore, we can say that the
left-hand side and the right-hand side are identical. So therefore, the answer is
yes. And we can say that the equation π₯
cubed minus π¦ cubed equals π₯ minus π¦ multiplied by π₯ squared plus π₯π¦ plus π¦
squared is an identity.