Related Topics: Operations on Algebraic Expressions

In these lessons, we will learn what variables, constants, terms, expressions and coefficients are in algebra.

The following diagram gives an example of algebraic expression. Scroll down the page for more examples.

### Algebraic Terms & Expressions

In mathematics, often the value of a certain number may be unknown. A **variable** is a symbol, usually a letter, which is used to represent an unknown number.

An**expression** can be term or a collection of terms separated by addition or subtraction operators. Some examples of expressions, with the numbers of terms, are listed below:

*x* + 2*y – *2*x* + 6 has four terms

### Coefficients Of Algebraic Terms

*x*)

**Terms of an Algebraic Expression**

A presentation of the terms of an algebraic expression.

The number and types of terms are presented.

Constants, variables and numerical coefficients, terms and expressions are discussed.**Parts of an expression and how to evaluate expressions**

This video shows the parts of an expression (terms, coefficients and variables) then explains about evaluating expressions using some examples.

What is a Term?

A term is any coefficient and its variable.

Identify the term in the expression:

4x - 2y + 5

Identify the coefficient and variable in the term:

7xy

Examples:

1. If x = 4 and y = 2

Evaluate 3x + 5y

2. Evaluate the expression if a = 7 and b = 2

(3 + a) - 2b

3. Jim and Jane like to go running in the morning. Jim runs twice as far as Jane. Let J be the distance Jane runs. What is expression for the combined distance they travel?**Simplifying Expressions and Combining Like Terms**

Expressions are put into their simplest form so as not to be confusing or too complex. One way of simplifying expressions is to combine like terms. By combining terms we can shorten and simplify our expressions, making them easier to read. Like terms often contain the same variable or variables.

This video shows how to simplify algebraic expressions by using the distributive property and combine like terms.

Examples:

1. Simplify 5x - 8 + 3(2x - 5)

2. Simplify 5y^{2} - y - (3y^{2} - 6y) + 8y

3. Simplify 9x^{3} + 5 - [5(x^{3} - 3) + 12]

**Algebraic Expression, Terms, and Coefficients**

In this video, you'll learn how to identify the parts of an expression in Algebra. You'll learn about expressions, terms, coefficients, and more.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

In these lessons, we will learn what variables, constants, terms, expressions and coefficients are in algebra.

The following diagram gives an example of algebraic expression. Scroll down the page for more examples.

Some examples of variables are:

x, a, t, y, b

A **term **can be a number, a variable, or a number and variable combined by multiplication or division.

Some examples of terms are:

x,8, 4y,

An

Expression | Number of Terms | Description |

6x |
1 | A number multiplied by a variable. The number is always written first followed by the variable(s). |

3w – 8 |
2 | Terms separated by – |

7b + 5t – 6 |
3 | Terms separated by + and – |

1 | All multiplication and division, no + or – symbol |

* Example: *

Determine the number of terms in the following expressions:

a) 5*xyz*

b) 3*x* + 2*y – *2*x* + 6

* Solution: *

a) 5*xyz* has one term

The number (positive or negative) in the algebraic term is called the **coefficient**.

** For example: **

For the term 4*x*, 4 is the coefficient

For the term –7*y*, –7 is the coefficient

The coefficient of 1 in an algebraic term is usually not written.

** For example: **

1*y* can be written as simply *y*. So, 1*y* and *y* are the same.

*Example: *

Find the coefficient and variable of each of the following terms:

a) 0.2*m *

b) –3*p *

c) *q *

d) *z *

e)

*Solution: *

a) 0.2*m *(The coefficient is 0.2 and the variable is *m*)

b) –3*p * (The coefficient is –3 and the variable is *p*)

c) *q* (The coefficient is and the variable is *q*)

d) *z* (The coefficient is 1 and the variable is *z*)

A presentation of the terms of an algebraic expression.

The number and types of terms are presented.

Constants, variables and numerical coefficients, terms and expressions are discussed.

This video shows the parts of an expression (terms, coefficients and variables) then explains about evaluating expressions using some examples.

What is a Term?

A term is any coefficient and its variable.

Identify the term in the expression:

4x - 2y + 5

Identify the coefficient and variable in the term:

7xy

Examples:

1. If x = 4 and y = 2

Evaluate 3x + 5y

2. Evaluate the expression if a = 7 and b = 2

(3 + a) - 2b

3. Jim and Jane like to go running in the morning. Jim runs twice as far as Jane. Let J be the distance Jane runs. What is expression for the combined distance they travel?

Expressions are put into their simplest form so as not to be confusing or too complex. One way of simplifying expressions is to combine like terms. By combining terms we can shorten and simplify our expressions, making them easier to read. Like terms often contain the same variable or variables.

This video shows how to simplify algebraic expressions by using the distributive property and combine like terms.

Examples:

1. Simplify 5x - 8 + 3(2x - 5)

2. Simplify 5y

3. Simplify 9x

In this video, you'll learn how to identify the parts of an expression in Algebra. You'll learn about expressions, terms, coefficients, and more.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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