Question

How many terms are there in the algebraic expression $7{x^3} + 2xy + z - 7y?$
A. $3$
B. $4$
C. $5$
D. $6$

Answer 1

Hint: We have to find the number of terms in the given algebraic expression. First we will understand the mathematical definition of the term. We should add the terms containing the same variable with the same degree in the given expression to get the correct answer. After that we will count the number of terms separated by the operators $( + )$ sign and $( - )$ sign.

Complete step by step answer:
As we know that in mathematics, a term is a single mathematical expression that can contain a single number, a single variable or several variables and numbers. As for example:
$5z,3,2{x^2},9{y^2}{z^3}$ are some of the mathematical terms.
If we have an expression such as
$2z + 5{x^2}$ , then we can say that in this expression we have two terms.
They are
$2z,5{x^2}$ .
Now in the given question we have
$7{x^3} + 2xy + z - 7y$ .
We can see that there are no such terms that contain the same variable with the same degree. So now we will count the number of terms that are separated by positive $( + )$ and negative sign i.e. $( - )$ .
So we can see that there are $4$ terms.
They are
$7{x^3},2xy,z,7y$ .

So, the correct answer is “Option B”.

Note:
We should note that if we have an expression like
$2x + 3z + 5y + 3x$ ,
then we should not get mistaken that there are four terms. We can see that we can add the two terms that contain the same variable $x$ .
So it can be written as
$2x + 3x + 3z + 5y = 5x + 3x + 5y$ .
Therefore it gives us the total number of terms $3$. They are
$5x,5y,3z$