Algebraic Expressions - Quick Notes

Variables and Constants

  • Variables: letters that represent numbers (unknowns); examples: x,y,zx, y, z
  • Constants: actual numbers; examples: 3,5,−23, 5, -2
  • Use: to express quantities with unknowns or fixed values

Algebraic Expressions

  • An algebraic expression is formed by combining variables and constants using the operations of addition, subtraction, multiplication, and division
  • Examples:
    • 3x3x
    • 5x+4y5x+4y
    • 5x2−4x−15x^2-4x-1
    • 3x+x3\sqrt{3}x+\sqrt{x^3}
    • x+3+x2x+3+x^2

Terms

  • A term is a variable, a constant, or the product of variables and constants
  • Examples: 3x2,  4xy,  5y2,  a2b3x^2,\; 4xy,\; 5y^2,\; a^2b
  • The denominators of terms can be constants as well as variables (e.g., 3x,  5y\frac{3}{x},\; \frac{5}{y})
  • In algebraic expressions, terms are connected together with addition or subtraction