# 1. Addition and Subtraction of Algebraic Expressions

Before we see how to **add and subtract integers**, we define **terms** and **factors**.

## Terms and Factors

A **term** in an algebraic expression is an expression
involving letters and/or numbers (called **factors**),
multiplied together.

### Example 1

The algebraic expression

5

x

is an example of **one** single **term**. It has **factors** 5 and *x*.

The 5 is called the **coefficient** of the
term and the *x* is a **variable**.

### Example 2

5*x* + 3*y *has **two** terms.

First term:5x, has factors `5` andx

Second term:3y, has factors `3` andy

The `5` and `3` are called the **coefficients** of the
terms.

### Example 3

The expression

`3x^2 - 7ab + 2esqrt(pi)`

has **three** terms.

First term:`3x^2` has factors `3` andx^{2}

Second term:`-7ab` has factors `-7`,aandb

Third Term:`2esqrt(pi)`; has factors `2`, `e`, and `sqrt(pi)`.

The `3`, `-7` and `2` are called **coefficients** of the
terms.

## Like Terms

"Like terms" are terms that contain the **same variables** raised to the **same
power**.

### Example 4

3*x*^{2} and 7*x*^{2} are **like terms.**

### Example 5

-8*x*^{2} and 5*y*^{2} are **not like terms**, because the variable is not the same.

## Adding and Subtracting Terms

**Important:** We can only add or subtract **like terms**.

**Why?** Think of it like this. On a table we have 4 pencils and 2 books. We cannot add the 4 pencils to the 2 books - they are not the same kind of object.

We go get another 3 pencils and 6 books. Altogether we now have 7 pencils and 8 books. We can't combine these quantities, since they are different types of objects.

Next, our sister comes in and grabs 5 pencils. We are left with 2 pencils and we still have the 8 books.

Similarly with algebra, we can only add (or subtract) similar "objects", or those with the same letter raised to the same power.

### Example 6

Simplify 13*x* + 7*y* − 2*x * + 6*a*

### Example 7

Simplify −5[−2(*m* − 3*n*) + 4*n*]

**Note:**

The fancy name for round brackets ( ) is "parentheses".

The fancy name for square brackets [ ] is "box brackets".

The fancy name for curly brackets { } is "braces".

### Example 8

Simplify −[7(*a* −
2*b*) − 4*b*]

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