Parts of an Expression

TERMS Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Each term in an algebraic expression is separated by + or – sign. 5x +3y + 8 What are the terms? The terms are 5x, 3y and 8.

COEFFICIENTS AND VARIABLE PARTS In a term like 7x, there are two parts: the numerical part and the variable part The numerical part is given a special name—it is called the coefficient of the term. Coefficient Variable

VARIABLES A variable is a symbol assigned to an unknown value. It is usually represented with letters such as x, y, or t. Often the letter used signifies what is being represented. For example, l stands for the length of a rectangle, w stands for the width of the rectangle, s for the number of students, t for time, etc. We use variables when we need to indicate how things are related even though we may not know the exact values of the things. For example, if we want to say that Joe earns 3 times what Sam earns, we can say j = 3s

In the term 4y, what is the coefficient? What is the variable? In the term 17x, what is the coefficient? What is the variable? 4 is the coefficient and y is the variable. 17 is the coefficient and x is the variable.

In the term 4y, what is the coefficient? What is the variable? In the term −7x 2 y, what is the coefficient? What is the variable? 4 is the coefficient and y is the variable. -7 is the coefficient and x 2 y is the variable.

COEFFICIENTS of 1 and -1 If you don't ‘see’ a coefficient, then it is 1. That is, x has a coefficient of 1. Also, x 2 has a coefficient 1. It's never necessary to write a coefficient of 1, because multiplication by 1 doesn't change anything. In the term −x, the coefficient is −1. In the term −x 2 y, the coefficient is also −1.

CONSTANTS

CONVENTIONAL WAY TO WRITE TERMS In any term, it is conventional to write the numerical coefficient FIRST. You should write 4xy, not xy4 or x4y. Also, it is conventional to write any variable(s) in ALPHABETICAL order. You write 5xy, not 5yx.