Question Video: Determining the Number of Terms an Algebraic Expression Consists of

How many terms are in the expression 4π‘₯ βˆ’ 𝑦² + 27?

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Video Transcript

How many terms are in the expression four π‘₯ minus 𝑦 squared plus 27?

To answer this question, we first need to recall what we mean by a term. And in mathematics, terms is one of those words which has many different definitions depending on the context. In this context, we’re asked for the number of terms in an algebraic expression. And this can mean one of two things. It could be the number of monomials in our expression, or it could also be the number of like expressions in our expression. In this case, both of these will give us the same answer. We’ll just use the number of monomials in our expression.

Remember, a monomial is the product between constants and variables raised to the power of nonnegative integers. We can see in our case there are three monomials in this expression. Four π‘₯ is a monomial because we can write π‘₯ as π‘₯ to the first power. Negative 𝑦 squared is a monomial because negative one is a constant and two is a nonnegative integer. Finally, 27 is a monomial because 27 is a constant. Therefore, because our expression contained three different monomials, we were able to show that there were three terms in this expression.

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