Expressions

Combinations of numbers, variables, and operations that represent a value.

Definition

An expression is a combination of numbers, variables, and operations that represents a value. Unlike an equation, an expression has no equals sign โ€” it's a phrase, not a sentence.

Examples:

  • 3+53 + 5 โ€” a numeric expression (evaluates to 88)
  • 2x+12x + 1 โ€” an algebraic expression (depends on xx)
  • x2โˆ’4x^2 - 4 โ€” a polynomial expression

Terms are the parts separated by ++ or โˆ’-. In 2x+12x + 1, the terms are 2x2x and 11.

Evaluating an expression

Evaluate 3x+23x + 2 when x=4x = 4:

3(4)+2=12+2=143(4) + 2 = 12 + 2 = 14

Substitute the value of xx, then simplify.

Identifying terms and coefficients

In 5x2โˆ’3x+75x^2 - 3x + 7:

  • Terms: 5x25x^2, โˆ’3x-3x, 77
  • Coefficient of x2x^2: 55
  • Coefficient of xx: โˆ’3-3
  • Constant term: 77
Try it

Evaluate 2aโˆ’b+32a - b + 3 when a=5a = 5 and b=2b = 2.

Solution
2(5)โˆ’2+3=10โˆ’2+3=112(5) - 2 + 3 = 10 - 2 + 3 = 11

Related concepts

Related reading