Expressions: Combining Like Terms
Master the foundational algebra skill tested on every SAT Math section
SAT Math — Algebra & Problem Solving
1. What Is an Algebraic Expression?
An algebraic expression is a combination of numbers, variables, and operations ($+, -, \times, \div$) that represents a mathematical relationship.
$3x + 5$
Two terms, one variable$2a^2 - 4a + 7$
Three terms, one variable$5xy + 3x - 2y$
Three terms, two variables2. Anatomy of a Term
Terms are the parts of an expression separated by $+$ or $-$ signs. Each term is a building block of the expression.
Example: In $3x^2 + 5x - 7$, there are three terms: $3x^2$, $5x$, and $-7$.
Parts of a Term
Coefficient
The numerical factor in front of the variable(s).
- In $5x^2y$: coefficient is 5
- In $-3a$: coefficient is −3
- In $x$: coefficient is 1 (invisible!)
- In $-x$: coefficient is −1
Variable Part
The letter(s) with their exponents.
- In $5x^2y$: variable part is $x^2y$
- In $-3a$: variable part is $a$
- In $7$: variable part is none (constant term)
Constant Term: A term with no variable — just a number. In $3x + 7$, the constant term is $7$. Its coefficient is the number itself.
