Basic Algebra | Adding and Subtracting 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

5x

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

5x + 3y has two terms.

First term: 5x, has factors $\displaystyle{5}$ and x
Second term: 3y, has factors $\displaystyle{3}$ and y

The $\displaystyle{5}$ and $\displaystyle{3}$ are called the coefficients of the terms.

Example 3

The expression

$\displaystyle{3}{x}^{2}-{7}{a}{b}+{2}{e}\sqrt{{\pi}}$

has three terms.

First term: $\displaystyle{3}{x}^{2}$ has factors $\displaystyle{3}$ and x²
Second term: $\displaystyle-{7}{a}{b}$ has factors $\displaystyle-{7}$, a and b
Third Term: $\displaystyle{2}{e}\sqrt{{\pi}}$; has factors $\displaystyle{2}$, $\displaystyle{e}$, and $\displaystyle\sqrt{{\pi}}$.

The $\displaystyle{3}$, $\displaystyle-{7}$ and $\displaystyle{2}$ are called coefficients of the terms.

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