Video: Factorizing a Difference of Two Squares

If 𝑥 − 𝑦 = 9 and 𝑥 + 𝑦 = 10, what is the value of 𝑥² − 𝑦²?

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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.

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