Question Video: Working with Polynomial Identities Mathematics

Video Transcript

Use the identity 𝑥 minus 𝑦 multiplied by 𝑥 plus 𝑦 is equal to 𝑥 squared minus 𝑦 squared to evaluate 33 squared minus 31 squared without a calculator.

If we consider the right-hand side of our identity, our value for 𝑥 in this question is 33 and 𝑦 is equal to 31. Substituting these values into the left-hand side of the identity gives us 33 minus 31 multiplied by 33 plus 31. 33 minus 31 is equal to two. 33 plus 31 is equal to 64. We need to multiply two by 64. This is equal to 128. Therefore, 33 squared minus 31 squared is 128.