Unlike Terms - Definition, Examples, Quiz, FAQ, Trivia
Learn to identify and work with like and unlike terms in algebraic expressions
What Are Algebraic Terms?
Algebraic terms are the building blocks of algebraic expressions. Each term is made up of:
1. Coefficient: The number part (like 4 in 4x)
2. Variable: The letter that represents an unknown value (like x or y)
3. Exponent: A small number that shows how many times to multiply the variable (like the 2 in x²)
A term can also be just a number with no variable - we call this a constant term. For example, in the expression 3x + 4y - 7, the terms are 3x, 4y, and -7.
Key Concept
Terms are separated by + or - signs. The expression 5x - 3y + 2 has three terms: 5x, -3y, and +2.
Understanding Like Terms
Like terms are terms that have exactly the same variables raised to the same exponents. Only the coefficients can be different.
Examples of like terms:
• 3x and 5x (both have the variable x)
• -2y² and 7y² (both have y²)
• 4 and 9 (both are constants with no variables)
Like terms can be combined together by adding or subtracting their coefficients. This helps us simplify expressions and solve equations more easily.
Like Terms
Same variable (x)
Like Terms
Same variable and exponent
Like Terms
Both constants
Understanding Unlike Terms
Unlike terms have different variables or different exponents. These terms cannot be combined by adding or subtracting because they represent different things.
Examples of unlike terms:
• 3x and 4y (different variables)
• 5x and 2x² (same variable but different exponents)
• 3xy and 2x (different combinations of variables)
• 7 and 4x (constant and variable term)
Unlike terms must stay separate in an expression. You can only combine them when they become like terms through simplification.
Unlike Terms
Different variables
Unlike Terms
Different exponents
Unlike Terms
Different variable combinations
Remember
Terms are unlike if they have different variables or different exponents. Only coefficients can be different for terms to be "like."
Combining Like Terms
Combining like terms is like organizing your toys - you put all the blocks together, all the cars together, etc. In algebra, we combine terms that have the same variables and exponents.
Steps to combine like terms:
1. Identify all the like terms in the expression
2. Add or subtract their coefficients
3. Keep the variable part unchanged
Example: Simplify 3x + 2y - x + 4
Step 1: Identify like terms - 3x and -x (both have x), 2y (only one y term), and 4 (constant)
Step 2: Combine x terms: 3x - x = 2x
Step 3: Write all terms together: 2x + 2y + 4
Notice that we couldn't combine 2x, 2y, and 4 because they're unlike terms.
Combining Like Terms
Examples of Unlike Terms
Let's look at some expressions and identify the unlike terms:
Example 1: 4x + 3y - 2x + 5
• Like terms: 4x and -2x (both have x)
• Unlike terms: 3y and 5 (different from x terms and from each other)
Simplified: (4x - 2x) + 3y + 5 = 2x + 3y + 5
Example 2: 3a² + 2b - 4a + 7
• Unlike terms: 3a², 2b, -4a, and 7 (all different variables/exponents)
This expression is already simplified - no like terms to combine.
Example 3: 5xy + 2x - 3y + 4
• Unlike terms: 5xy, 2x, -3y, and 4 (all different variables)
This expression cannot be simplified further.
Example 4: 2x + 3x² - 4x + x²
• Like terms: 2x and -4x (both x), 3x² and x² (both x²)
Simplified: (2x - 4x) + (3x² + x²) = -2x + 4x²
Practice Tip
When identifying like terms, always look at the variable AND its exponent. 3x and 3x² are unlike terms because the exponents are different.
Practice Quiz
Test your understanding of like and unlike terms with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about 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 by the Persian mathematician Muhammad ibn Musa al-Khwarizmi in the 9th century.
Variables in Science
Algebraic terms with variables are used in all sciences. For example, Einstein's famous equation E = mc² uses variables to represent energy (E), mass (m), and the speed of light (c).
Algebra in Space Travel
NASA engineers use algebraic expressions with many terms to calculate rocket trajectories. A single miscalculation in combining terms could send a spacecraft off course!
Longest Equation
The longest mathematical equation ever written contains over 200 trillion terms! It would take light nearly 6 years to travel from one end to the other if printed in standard font size.
