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

9x

is an example of one single term. It has factors 9 and x.

The 9 is called the coefficient of the term.

Example 2:

5x + 3y has two terms.

First term: 5x, has factors 5 and x

Second term: 3y, has factors 3 and y

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

Example 3:

3x² − 7ab + 2e√π has three terms.

First term: 3x²; has factors 3 and x²

Second term: -7ab; has factors -7, a and b

Third Term: 2e√π; has factors 2, e and √π

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.

Examples

3x² and 7x² are like terms.

-8x² and 5y² 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 1

Simplify 13x + 7y − 2x + 6a

Answer

Example 2

Simplify -2[-3(x - 2y) + 4y]

Answer

Here is a LiveMath document which allows you to play with this question.

LIVEMath

Example 3

Simplify - [7(a- 2b) − 4b]

Answer

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