Which terms are like terms in the following expression? [tex]3 x+3 x y-2 x+5 y+5 x^2[/tex]
A. [tex]3 x, 3 x y,-2 x[/tex] and [tex]5 y[/tex]
B. [tex]3 x[/tex] and [tex]-2 x[/tex]
C. [tex]3 x,-2 x[/tex] and [tex]5 x^2[/tex]
D. All terms are alike.

The like terms are 3 x and − 2 x , so the answer is 3 x and − 2 x ​ .

Explanation

Identifying Like Terms We are given the expression 3 x + 3 x y − 2 x + 5 y + 5 x 2 and asked to identify the like terms. Like terms are terms that have the same variable raised to the same power.

Analyzing Each Term Let's examine each term:



3 x is a term with the variable x raised to the power of 1.
3 x y is a term with the variables x and y .
− 2 x is a term with the variable x raised to the power of 1.
5 y is a term with the variable y raised to the power of 1.
5 x 2 is a term with the variable x raised to the power of 2.


Determining Like Terms From the analysis above, we can see that 3 x and − 2 x are like terms because they both have the variable x raised to the power of 1.

Final Answer Therefore, the like terms in the expression are 3 x and − 2 x .


Examples
Understanding like terms is essential in simplifying algebraic expressions. For instance, if you're calculating the total cost of items, you can only combine the costs of items that are of the same type. If you have 3 apples and buy 2 more, you now have 5 apples. This is because 'apples' are the like term. Similarly, in algebra, you can combine like terms to simplify equations and make them easier to solve. For example, if you have 3 x + 2 x , you can combine them to get 5 x .

Answered by GinnyAnswer | 2025-07-05

The like terms in the expression 3 x + 3 x y − 2 x + 5 y + 5 x 2 are 3 x and − 2 x because they both contain the variable x raised to the same power. Therefore, the chosen option is B. 3 x and − 2 x .
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Answered by Anonymous | 2025-08-18