### Video Transcript

If π₯ squared plus nine π¦ squared equals 15 and π₯π¦ equals two, what is the value of π₯ minus three π¦ squared?

At first, it might not be really clear what the best path for solving this is. You might want to factor π₯ squared plus nine π¦ squared equals 15 to see if it would give us something similar to π₯ minus three π¦ squared. However, π₯ squared plus nine π¦ squared equals 15 doesnβt fit any of our algebraic identities.

So what Iβm gonna do is rewrite π₯ minus three π¦ squared as π₯ minus three π¦ times π₯ minus three π¦. We can expand and multiply here. π₯ times π₯ equals π₯ squared. π₯ times negative three π¦ equals negative three π₯π¦. Negative three π¦ times π₯ equals negative three π₯π¦. And negative three π¦ times negative three π¦ equals positive nine π¦ squared.

Negative three π₯π¦ and negative three π₯π¦ are like terms. We can combine them by adding their coefficients. Negative three plus negative three equals negative six. Bring down the π₯π¦. And we found that π₯ minus three π¦ squared equals π₯ squared minus six π₯π¦ plus nine π¦ squared. We know the value of π₯π¦. And we know the value of π₯ squared plus nine π¦.

We can rearrange the equation to say π₯ squared plus nine π¦ squared minus six π₯π¦ and then substitute what we know. We know that π₯ squared plus nine π¦ squared equals 15. We also know that π₯ times π¦ equals two. We now have 15 minus six times two. 15 minus 12 equals three.

π₯ minus three π¦ squared is equal to three.