How many terms are in the
expression four 𝑥 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 𝑥 is a monomial because we
can write 𝑥 as 𝑥 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.