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Question Video: Factorizing a Difference of Two Squares Mathematics • 9th Grade

If π‘₯ βˆ’ 𝑦 = 9 and π‘₯ + 𝑦 = 10, what is the value of π‘₯Β² βˆ’ 𝑦²?

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Video Transcript

If π‘₯ minus 𝑦 equals nine and π‘₯ plus 𝑦 equals 10, what is the value of π‘₯ squared minus 𝑦 squared?

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

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

Given that π‘₯ minus 𝑦 equals nine and π‘₯ plus 𝑦 equals 10, π‘₯ squared minus 𝑦 squared equals 90.

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