Adding and Subtracting Terms

In short: You can only add or subtract like terms. Add or subtract the numbers in front and keep the letters the same, so $3x+5x=8x$, but $3x+5y$ stays as it is.

Before you start

• Like terms have the same letters with the same powers, such as $3x$ and $7x$. (See the chapter Terms, Like Terms and Notation.)
• $x$ on its own means $1x$.
• Adding and subtracting with negative numbers, for example $3-5=-2$. (Covered fully in Negative and Positive Numbers.)

Only like terms can be combined

Why does it work? $5x$ is five lots of $x$ and $3x$ is three lots of $x$. Together that is eight lots of $x$, just like 5 apples and 3 apples make 8 apples.

Unlike terms stay apart

$3x+4y$ cannot be made shorter. Apples and bananas do not combine into "7 apple-bananas".

$$3x+4y+2x^2-2y=3x+2x^2+2y$$

Here only the $y$ terms combine, because $4y-2y=2y$. The $3x$ and $2x^2$ are unlike, so they stay as they are.

Simplifying longer expressions

Follow these steps:

1. Underline or circle each group of like terms. Use a different mark for each group.
2. Keep the sign in front of each term with it. The sign belongs to the term on its right.
3. Add up each group.
4. Write the answer, usually letters in alphabetical order and the plain number last.

Quick summary

• Only like terms can be added or subtracted.
• Add or subtract the numbers in front. The letters and powers do not change.
• Each term takes the sign in front of it.
• Unlike terms are left as they are.
• A group can add to zero and disappear.
• Check by putting in an easy number for each letter.

Quiz