Like Terms
Like terms are algebraic terms with identical variable parts that can be combined in Grade 8 math (Yoshiwara Core Math). Terms with the same variable raised to the same power are like terms: 3x and 7x combine to 10x. Unlike terms (3x and 3x²) differ in exponent and cannot be combined. Constants combine with constants. Combining like terms is the fundamental simplification step in algebra, required for solving equations, expanding expressions, and polynomial operations.
Key Concepts
Property Like terms are terms where the variable part is the same. The numbers multiplied by the variable are called the coefficients.
To add or subtract like terms: 1. Add or subtract the coefficients. 2. Do not change the variable part of the terms.
Examples To combine $8m 3m$, we subtract the coefficients: $(8 3)m = 5m$. To combine $7ab + 5ab$, we add the coefficients: $(7+5)ab = 12ab$. To combine $y + 9y$, remember the coefficient of $y$ is 1. So, $(1+9)y = 10y$.
Common Questions
What are like terms?
Terms with the same variable(s) raised to the same power(s). 3x and −5x are like terms; 3x and 3x² are not.
How do you combine like terms?
Add or subtract the coefficients, keep the variable part. 3x + 7x = 10x.
Can constants combine with variable terms?
No. Constants combine only with other constants. 5 + 3x cannot be simplified.
What is the coefficient?
The number in front of the variable. In 7x, the coefficient is 7. In −3y², it is −3.
Why can't 3x and 3x² combine?
They represent different quantities: 3x is 3 groups of x; 3x² is 3 groups of x². Different exponents = unlike terms.