Question

Number of terms in expression \[3{x^2}y - 2{y^2}z - {z^2}x + 5\] is
A). 2
B). 3
C). 4
D). 5

Answer 1

Hint: In this question, we have to find the number of terms. So, first we will understand the mathematical definition of the word ‘term’. And then, for the given expression, add the terms if they are containing the same variable and leave the other terms of other variables as it is. Count the number of terms that are separated by the operations positive or negative sign to get the answer.

Complete step-by-step solution:
Here, we have been provided with an expression \[3{x^2}y - 2{y^2}z - {z^2}x + 5\] and we are asked to find the total number of terms present in the expression. But before starting the solution we will discuss the definition of ‘term’.
A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression $4x + y$ , the two terms are $4x$ and $y$ .
Now, we will find the number of terms which are in the expression \[3{x^2}y - 2{y^2}z - {z^2}x + 5\] and for that first we have to add the terms containing the same variable. But in this case, the terms do not have the same variable. So, we will directly count the number of terms which are separated by positive and negative signs. The terms are \[3{x^2}y\] , \[2{y^2}z\], \[{z^2}x\], $5$. So, the number of terms is 4.
Hence, option (3) is the correct answer.

Note: In this case, we didn’t add the terms because the variable of the terms was not the same. But if in some questions the variable of more than 1 term is the same. Then, we have to add them up and after that follow the procedure done in the solution above.
An algebraic expression is a mathematical phrase that contains integral or fractional constants (numbers), variables (alphabets) and algebraic operators (such as addition, subtraction, division, multiplication, etc.) operating on them. Also, these expressions are expressed in the form of term, factor and coefficient.