Like and Unlike Algebraic Terms - Definition, Examples, Quiz, FAQ, Trivia
Learn to identify and work with algebraic terms through simple explanations and practice activities
What are Algebraic Terms?
In algebra, a term is a single mathematical expression that could be a number, a variable, or numbers and variables multiplied together. Terms are separated by + or - signs in an expression.
For example, in the expression 3x + 2y - 5, there are three terms: 3x, 2y, and 5.
Each term has:
- A coefficient (the number part)
- A variable (the letter part)
- An exponent (how many times the variable is multiplied by itself)
Key Concept
Algebraic terms are the building blocks of algebraic expressions. Understanding them helps us simplify and solve equations.
What are Like Terms?
Like terms are terms that have the exact same variables raised to the exact same exponents. Only the coefficients can be different.
Like Terms Rule
Terms with identical variable parts can be combined through addition or subtraction.
3x and 5x are like terms because they both have the variable x raised to the same power (1).
2y² and 7y² are like terms because they both have y².
4ab and 6ab are like terms because they both have the same variables a and b.
Remember
The coefficients don't need to match for terms to be "like terms." Only the variable parts must be identical.
What are Unlike Terms?
Unlike terms are terms that have different variables or the same variables but with different exponents.
Unlike Terms Rule
Terms with different variable parts cannot be combined through addition or subtraction.
3x and 5y are unlike terms because they have different variables.
2x² and 7x are unlike terms because the exponents are different (x² vs x).
4ab and 6a are unlike terms because they don't have the exact same variables.
Important
Unlike terms cannot be combined through addition or subtraction. You can only combine like terms.
Examples of Like and Unlike Terms
Let's look at more examples to understand the difference between like and unlike terms:
Like Terms Examples
Unlike Terms Examples
Notice that regular numbers without variables (like 9 and 15) are considered like terms with each other because they both have no variables. They can be combined through addition or subtraction.
Practice Tip
When identifying like terms, look carefully at both the variables and their exponents. They must match exactly.
Practice Quiz
Test your understanding with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about like and unlike terms:
Algebra Trivia
Discover interesting facts about algebra and mathematical terms:
Origin of Algebra
The word "algebra" comes from the Arabic word "al-jabr" which means "reunion of broken parts." It was first used in the title of a book written by the Persian mathematician Muhammad ibn Musa al-Khwarizmi around 820 AD.
Why We Use x in Algebra
The use of x as an unknown variable in algebra might come from Spanish Arabic scholars who used the word "shay" (thing) for unknowns. This was translated to Spanish as "xei," which was abbreviated to x.
The Longest Equation
The longest mathematical equation ever written contains about 200 terabytes of text! It would take approximately 4.5 billion pages to write it out. Thankfully, algebra helps us write complex ideas in simple terms.
Algebra in Daily Life
We use algebra more often than we realize! When we calculate discounts while shopping, determine cooking measurements for recipes, or figure out travel time, we're using algebraic thinking without even knowing it.
