Question Video: Identifying Using the Language of Algebra Mathematics

Video Transcript

Identify whether 𝑥 minus 𝑦 all squared equals 𝑥 squared minus two 𝑥𝑦 plus 𝑦 squared is an expression, an identity, a formula, or an inequality.

Let’s have a look at this statement 𝑥 minus 𝑦 all squared equals 𝑥 squared minus two 𝑥𝑦 plus 𝑦 squared. If we take a look at the left-hand side, this would be composed of the set of parentheses 𝑥 minus 𝑦 times 𝑥 minus 𝑦. We could expand these parentheses, for example, using the FOIL method. We would get 𝑥 squared minus two 𝑥𝑦 plus 𝑦 squared, which means that we have a left-hand side which is equal to the right-hand side. So this will be true for any values of 𝑥 or 𝑦. It doesn’t matter what values we choose; the left-hand side will always be equal to the right-hand side. The word we use for a statement like this would be an identity.

Sometimes when we have an identity, instead of having this equals to symbol, we could use the identity symbol. But we don’t always need to write it, so we can’t use it really as an indicator if something is an identity or not. If we look at the other options we’re given, we can say that our statement is not an expression, as the expression would be the collection of terms that we have either on the left-hand side or on the right-hand side. A formula is a type of equation that we might use to help us find the value of a variable, given how another variable has changed. An example of a formula might be, for example, the circumference of a circle is equal to 𝜋 times the diameter. This isn’t quite what we have in our statement.

Finally, if we had an inequality, we’d be looking for one of the symbols, for example, less than or greater than or equal to. And we haven’t got one of these in our statement. We can then give our answer that 𝑥 minus 𝑦 squared equals 𝑥 squared minus two 𝑥𝑦 plus 𝑦 squared is an identity.