Algebraic Expressions

Expression: A combination of numbers, variables, and operations (no equals sign). Example: $3x + 5$. Unlike equations, expressions don't have an equals sign.

Variable: A letter representing an unknown number. Common variables: $x, y, n, a, b$, etc. Variables can represent any number.

Coefficient: The number multiplying a variable. In $5x$, $5$ is the coefficient. If no number is shown, the coefficient is $1$ (e.g., $x = 1x$).

Constant: A number without a variable. In $3x + 7$, $7$ is the constant term. Constants don't change when variables change.

Term: Parts separated by $+$ or $-$. $3x + 5$ has two terms: $3x$ and $5$. $2x^2 - 3x + 1$ has three terms.

Like terms: Terms with the same variable and exponent. $3x$ and $5x$ are like terms (both have $x$ to the first power). $3x$ and $3x^2$ are NOT like terms (different exponents).

Expression vs. Equation: Expression: $3x + 5$ (no equals sign). Equation: $3x + 5 = 17$ (has equals sign, can be solved).