### Video Transcript

If 𝑥 minus 𝑦 equals nine and 𝑥
plus 𝑦 equals 10, what is the value of 𝑥 squared minus 𝑦 squared?

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

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

Given that 𝑥 minus 𝑦 equals nine
and 𝑥 plus 𝑦 equals 10, 𝑥 squared minus 𝑦 squared equals 90.