Combining Like Terms

Need some basic practice with terms and coefficients first? Identifying Variable Parts and Coefficients of Terms

Terms with the same variable part are called like terms because they look ‘alike’ as far as the variable part is concerned. The phrase like terms can refer to two or more terms.

Thus, $\,2x\,$ and $\,-5x\,$ are like terms. In each term, the variable part is $\,x\,.$

Also, $\,x^2\,,$ $\,\frac{1}{3}x^2\,,$ and $\,(4.2)x^2\,$ are like terms. In each term, the variable part is $\,x^2\,.$

Only like terms can be combined, and they are combined by adding the coefficients. For example:

$\,2x + 5x = (2 + 5)x = 7x\,$

and

$\,7y - 4y = (7 - 4)y = 3y\,$

You might want to think of these in concrete terms: Two x-rays plus five x-rays is seven x-rays. Seven yo-yos minus four yo-yos is three yo-yos.

Terms that are not like terms cannot be combined. For example, there is no simpler way to write $\,2x + 5y\,$ or $\,y - 2y^2\,.$

Examples

Question: Combine like terms:  $\,2x - 3y + x + 5y$

Answer: $3x + 2y$
Note: The variable $\,x\,$ occurs first in the original expression, and it must be written first in the answer, to be recognized as correct by this exercise. (That is, $\,2y + 3x\,$ is not recognized as a correct answer.)

Question: Combine like terms:  $\,x^2 - 3xy - 4x^2 + 5y + xy - 6y$

Answer: $-3x^2 - 2xy - y$
Note: In the original expression, moving from left to right and looking for different term types, $\,x^2\,$ comes first, $\,xy\,$ next, and $\,y\,$ last. They must be written in this order in your answer, to be recognized as correct.

In the exercise below, exponents are written using the ‘ ^ ’ key.

Question: Combine like terms:  $\,2t + 4w - 3w + t - w$

Answer: $3t$
Note: If a term has a coefficient of $\,0\,$ (like $\,4w - 3w - w\,$), then it will not appear in your final answer.

Practice