### Video Transcript

If ๐ฅ minus ๐ฆ equals nine and ๐ฅ
plus ๐ฆ equals 10, what is the value of ๐ฅ squared minus ๐ฆ squared?

The key here is recognizing ๐ฅ
squared minus ๐ฆ squared as one of our identities. It is the difference of
squares. And ๐ squared minus ๐ squared,
subtracting one square from another, can be written as ๐ plus ๐ times ๐ minus
๐.

Therefore, we can take ๐ฅ squared
minus ๐ฆ squared and write it as ๐ฅ plus ๐ฆ times ๐ฅ minus ๐ฆ. We know that ๐ฅ plus ๐ฆ equals 10
and that ๐ฅ minus ๐ฆ equals nine. 10 times nine equals 90.

Given that ๐ฅ minus ๐ฆ equals nine
and ๐ฅ plus ๐ฆ equals 10, ๐ฅ squared minus ๐ฆ squared equals 90.