Video Transcript
If π₯ minus π¦ equals nine and π₯
plus π¦ equals 10, what is the value of π₯ squared minus π¦ squared?
The key here is recognizing π₯
squared minus π¦ squared as one of our identities. It is the difference of
squares. And π squared minus π squared,
subtracting one square from another, can be written as π plus π times π minus
π.
Therefore, we can take π₯ squared
minus π¦ squared and write it as π₯ plus π¦ times π₯ minus π¦. We know that π₯ plus π¦ equals 10
and that π₯ minus π¦ equals nine. 10 times nine equals 90.
Given that π₯ minus π¦ equals nine
and π₯ plus π¦ equals 10, π₯ squared minus π¦ squared equals 90.