Algebraic Expressions

Definition

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like $x$ or $y$), and operators (like add, subtract, multiply, and divide).

Why It Matters

Expressions are the “sentences” of mathematics. Without the ability to construct and manipulate these symbolic representations, we cannot describe the relationships between physical quantities or build the models required for engineering, physics, and finance.

Core Concepts

• Variables: Symbols used to represent unknown or changing values.

  • Example: $x$, $y$
  • How to read: “x” or “y” as placeholders for unknown or varying quantities.
  • Meaning: Stand in for numbers you don’t know yet or that can take many values.

• Terms: Parts of an expression separated by $+$ or $-$ signs (e.g., $3x$ and $5$ in $3x + 5$).

  • How to read: “Three x and five in three x plus five.”
  • Meaning: Each term is one “chunk” of the expression; $3x$ and $5$ are unlike terms and cannot be combined.

• Coefficients: The numerical part of a term with a variable (e.g., $3$ in $3x$).

  • How to read: “Three in three x.”
  • Meaning: The multiplier attached to the variable—how many “copies” of $x$ the term contains.

Connected Concepts

• Elementary Algebra
• Variables
• Constants
• Polynomials: Basic Operations
• Rational Expressions