Like terms
Like Terms is a Grade 8 algebra skill in Saxon Math Course 3, Chapter 4, where students learn that like terms are terms with the same variable raised to the same exponent and can be combined by adding or subtracting their coefficients. Identifying and combining like terms is a fundamental step in simplifying algebraic expressions and solving equations.
Key Concepts
Property Like terms have identical variable parts, including exponents. The variables may appear in any order.
Examples Like terms: $ 5xy$ and $yx$ are like terms because they share the identical variable part $xy$. Unlike terms: $2xy$ and $ 5x^2y$ are unlike because the exponents on $x$ are different (1 vs. 2). Like terms: $4a^2b$ and $ a^2b$ are like terms because the variable part $a^2b$ is identical.
Explanation Imagine variables are secret family names. The term 3xy is from the 'xy' family, and so is yx since the order of variables doesn't matter! But x^2y is a different family because the exponent changes the name. You can only combine terms that belong to the exact same family tree, including their exponents, to keep things tidy.
Common Questions
What are like terms in algebra?
Like terms are terms that have the same variable or variables raised to the same exponents. For example, 3x and 7x are like terms because they both have x to the first power.
How do you combine like terms?
Add or subtract the coefficients (the numbers in front) of the like terms while keeping the variable part unchanged. For example, 5x + 3x = 8x.
Why can you only combine like terms?
Only like terms represent the same kind of quantity. Adding 3x and 4y would be like adding apples and oranges; the result cannot be simplified further.
What makes two terms unlike terms?
Two terms are unlike if they have different variables or if the same variable is raised to different exponents. For example, 3x and 3y are unlike, and 2x squared and 2x are unlike.
Where are like terms taught in Grade 8?
Like terms are covered in Saxon Math Course 3, Chapter 4: Algebra and Measurement.