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

Video Transcript

If 𝑥 plus 𝑦 is equal to two and 𝑥 minus 𝑦 equals six, what is the value of 𝑥 squared minus 𝑦 squared?

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