Algebraic Terms Definition
To identify algebraic terms, the definition of the word terms is needed first of all. In algebra, terms are separated by a plus or minus sign in an expression.
For an in-depth explanation, please scroll down.
Terms of an Algebraic Expression – Exercises
Instructions: Consider algebraic terms below and answer the questions that follow. You may want to see the explanations below first.
4a2 + 16ab + 24b4 – 8
1) Is the above statement an expression, equation, or inequality?
2) Identify the variables.
3) Identify the coefficients.
4) Identify the constant.
5) Identify the greatest common factor and express in factored form.
Terms of an Algebraic Expression – Answers
1) The statement is an expression since it does not have the equals sign.
It also does not have the greater than or less than sign.
2) The variable in the first term is a.
The variables in the second term are a and b.
The variable in the third term is b.
3) The coefficient in the first term is 4.
The coefficient in the second term is 16.
The coefficient in the third term is 24.
4) The constant is –8.
5) The greatest common factor is 4. Factor as shown below.
4a2 + 16ab + 24b4 – 8 =
(4 × a2) + (4 × 4 × ab) + (4 × 6 × b4) + (4 × –2) =
4[(4 × a2) + (4 × 4 × ab) + (4 × 6 × b4) + (4 × –2)] =
4(a2 + 4ab + 6b4 – 2)
What are Algebraic Terms?
Algebraic terms are used to form algebraic expressions.
Algebraic terms consist of variables, coefficients, exponents, and constants.
Algebraic Terms Are Separated by Signs
Algebraic terms are separated by the addition or subtraction signs.
Variables: Variables are the letters, such as x or y, in an algebraic expression.
Coefficients: Coefficients are the numbers directly in front of the variables, such as the 4 in the term 4x2 or the 7 in the term 7y3.
Exponents: Exponents are the powers in an algebraic expression, such as the 2 in the term 4x2 or the 3 in the term 7y3.
Constants: Constants are the numbers without variables in an algebraic expression.
Terms can be used to create expressions, equations, and inequalities in algebra.
Expressions: Expressions are used to create equations and inequalities in algebra.
Equations: An algebraic equation must have the equals sign.
Inequalities: An algebraic inequality must have the less than or greater than sign.
Algebraic Terms Separated By the Plus Sign – Examples
Here is an algebraic expression:
4x2 + 7y3 + 3
If we add an equals sign and a value we get an algebraic equation:
4x2 + 7y3 + 3 = 0
If we add the less than or greater than sign and a value to our algebraic expression we get an algebraic inequality:
4x2 + 7y3 + 3 < 5
Algebraic Terms Separated By the Plus and Minus Signs – Examples
Look at the following algebraic expression as an illustration of algebraic terms.
3x2 + 9xy + 15y3 – 6
The first algebraic term is 3x2.
It consists of the variable x, the coefficient 3, and the exponent 2.
The second algebraic term is 9xy.
It consists of the variable x, the variable y, and the coefficient 9.
The third algebraic term is 15y3
It consists of the variable y, the coefficient 15, and the exponent 3.
The fourth algebraic term is –6.
The fourth term is a constant since it does not contain a variable.
Remember that you can identify your term as a negative if the term is preceded by the minus sign.
How to factor terms in algebraic expressions
You will also need to know how to factor expressions and equations by finding common factors in the algebraic terms.
In order to factor our equation, we take out the greatest common factor as shown below:
3x2 + 9xy + 15y3 – 6 =
3(x2 + 3xy + 5y3 – 2)
Terms of Algebraic Expressions – Further Practice
If you do not understand how to perform the operation illustrated above, you should also view the following posts.
Finding the Greatest Common Factor
Algebraic terms are also used to create quadratic expressions.
You should also view our posts on binomials, trinomials, and polynomials.
