Question

State true or false and give reasons for your answer.
$7{x^2}$ And 2x are unlike terms

Answer 1

Hint – In this question observe the power of the variable x in the given terms of $7{x^2}$ and 2x. If the power of variables is the same then they can be categorized into like terms else they are unlike terms. This concept will help get the right answer.

Complete step-by-step answer:
Like terms - Like terms are those terms which have the same variable along with the same raise to power for example if we talk about two different terms like ${x^2},2{x^2}$. Here the coefficients are different but the variable along with the respective power is the same. So this comes under the category of like terms.
Unlike terms - Unlike terms are those terms which don’t have the same variable along with the same raise to power for example if we talk about two different terms like ${x^3},2{y^2}$. Here the coefficients are different and the variable along with the respective power is also different . So this comes under the category of unlike terms.

As we know in mathematics terms are the variables which have the same power.
For example: 2x, 3x, 4x and so on....
Similarly ${x^2},2{x^2},3{x^2}.........$are like terms
So we can add like terms to make new like terms.
$x + 2x = 3x$
But when we add unlike terms there is a dead end as we cannot further simplify it
Now given terms are $7{x^2}$ and 2x,
So if we add them we get $7{x^2} + 2x$ which is a dead end we cannot further simplify it.
So the given statement is true.
So this is the required answer.

Note – There is a misconception about like terms that their two terms with same coefficients are like terms, this is absolutely equal coefficients criteria is never taken into consideration while commenting upon like and unlike terms. If the highest power of coefficients along with the variable and the coefficients all are the same then the terms are equal. It can be said that equal terms are like as well but like terms aren’t equal all the time.