# 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

Terms must be written in the order the term types appear, from left-to-right, in the original expression. Use the ‘ ^ ’ key for exponents.