Question Video: Evaluating Algebraic Expressions Using Factoring a Difference of Two Squares

If π‘₯ + 𝑦 = 2 and π‘₯ βˆ’ 𝑦 = 6, what is the value of π‘₯Β² βˆ’ 𝑦²?

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Video Transcript

If π‘₯ plus 𝑦 is equal to two and π‘₯ minus 𝑦 equals six, what is the value of π‘₯ squared minus 𝑦 squared?

The expression π‘₯ squared minus 𝑦 squared is known as the difference of two squares. This factors or factorizes into two parentheses or brackets: π‘₯ plus 𝑦 multiplied by π‘₯ minus 𝑦. In this question, we’re told that π‘₯ plus 𝑦 is equal to two and π‘₯ minus 𝑦 is equal to six. Multiplying these numbers gives us an answer of 12. If π‘₯ plus 𝑦 is equal to two and π‘₯ minus 𝑦 is equal to six, then π‘₯ squared 𝑦 squared is equal to 12. It is the product of these two numbers.

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