Question Video: Factorizing a Difference of Two Squares | Nagwa Question Video: Factorizing a Difference of Two Squares | Nagwa

# Question Video: Factorizing a Difference of Two Squares Mathematics

If ๐ฅ โ ๐ฆ = 9 and ๐ฅ + ๐ฆ = 10, what is the value of ๐ฅยฒ โ ๐ฆยฒ?

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### Video Transcript

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

The key here is recognizing ๐ฅ squared minus ๐ฆ 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 ๐ฅ squared minus ๐ฆ squared and write it as ๐ฅ plus ๐ฆ times ๐ฅ minus ๐ฆ. We know that ๐ฅ plus ๐ฆ equals 10 and that ๐ฅ minus ๐ฆ equals nine. 10 times nine equals 90.

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

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