Question Video: Identifying Using the Language of Algebra | Nagwa Question Video: Identifying Using the Language of Algebra | Nagwa

Question Video: Identifying Using the Language of Algebra Mathematics

Identify whether (π₯ β π¦)Β² = π₯Β² β 2π₯π¦ + π¦Β² is an expression, an identity, a formula, or an inequality.

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Video Transcript

Identify whether π₯ minus π¦ all squared equals π₯ squared minus two π₯π¦ plus π¦ squared is an expression, an identity, a formula, or an inequality.

Letβs have a look at this statement π₯ minus π¦ all squared equals π₯ squared minus two π₯π¦ plus π¦ squared. If we take a look at the left-hand side, this would be composed of the set of parentheses π₯ minus π¦ times π₯ minus π¦. We could expand these parentheses, for example, using the FOIL method. We would get π₯ squared minus two π₯π¦ plus π¦ 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 π₯ or π¦. It doesnβ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 donβt always need to write it, so we canβt use it really as an indicator if something is an identity or not. If we look at the other options weβ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 isnβt quite what we have in our statement.

Finally, if we had an inequality, weβd be looking for one of the symbols, for example, less than or greater than or equal to. And we havenβt got one of these in our statement. We can then give our answer that π₯ minus π¦ squared equals π₯ squared minus two π₯π¦ plus π¦ squared is an identity.

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