Question

How many terms are there in the expression: - \[2x-5y+3+x\]?

Answer 1

Hint: First understand the mathematical definition of the word ‘term’. Now, for the given expression, add the terms 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 operators (+) sign and (-) sign to get the answer.

Complete step by step answer:
Here, we have been provided with the expression: - \[2x-5y+3+x\] and we are asked to determine the total number of terms present in the expression. But first we need to understand the mathematical definition of the word ‘term’. So, let us see.
In mathematics, a term is a single mathematical expression that can contain a single number, a single variable, several numbers and variables multiplied together. For example: - \[2,5z,3{{x}^{2}},9{{x}^{2}}{{y}^{6}}{{z}^{3}}\]. As we can see that in the given examples, we do not have used any (+) sign or (-). This is because these two operators separate the given terms in an expression. For example: - \[5{{m}^{2}}+6n\], here we have two terms, i.e., \[5{{m}^{2}}\] and 6n, separated by (+) sign.
Now, let us come to the question. We have the expression: - \[2x-5y+3+x\]. Here, we can see that there are two terms that contain the same variable x, so they can be added. Therefore, the expression becomes: - \[3x-5y+3\]. Now, here we have the terms 3x, 5y and the constant term 3 separated by (-) sign and (+) sign respectively. So, 3x, 5y and 3 are the three different terms of the expression.

Hence, there are three terms in the provided expression.

Note: You may note that in the initial expression it looks like there are four terms present there. But as you can see that two of them have the same variable x and that is why they can be added. You must be careful about this point. Always remember that mathematical operators like multiplication and division do not separate the variables of an expression but only addition and subtraction does.