Algebra Expressions Flashcards

An algebraic expression consists of numbers, operations, and one or more symbols.
Examples of algebraic expressions include:
- 2n + 5
- 6(4d)
- 2 - 8d²
- 5n³ ÷ 6y²

Non-examples exclude expressions that are not algebraic, such as:
- Standalone numbers (e.g., 145)
- Equations (e.g., 8x + 15 = 55)
- Fractions (e.g., ¾)
- Equalities with algebraic terms (e.g., 3x³ ÷ 4y² = 124)

Parts of an algebraic expression are called terms.
Terms are separated by addition or subtraction signs, illustrated by the expression 3 + 2x + 7y, which consists of three terms: 3, 2x, and 7y.

Variable: Letters representing one or more unknown numbers (e.g., in 3 + 2x + 7y, x and y are variables).
Coefficient: The numerical factor of a term with a variable (in 3 + 2x + 7y, coefficients are 2 and 7).

A constant is a term without a variable. Example: In 3 + 2x + 7y, the constant is 3.

The expression n⁵ represents n multiplied by itself five times: n × n × n × n × n.
In the expression 5x⁴, the base is x and the exponent is 4 (with 5 as the coefficient).

Terms, coefficients, and constants breakdown:
- For 12 + 10c:
  - Terms: 12, 10c
  - Coefficient: 10
  - Constant: 12
- For 15 + 3w + ½:
  - Terms: 15, 3w, ½
  - Coefficient: 3
  - Constants: 15, ½
- For z² + 9w - 2:
  - Terms: z², 9w, -2
  - Coefficients: 9, 1 (in front of z)
  - Constant: -2
- For 6r(8r - 13):
  - Terms: 8r, 13
  - Coefficients: 6, 8
  - Constant: 13
- For 4x² - 7y + ¾:
  - Terms: 4x², -7y, ¾
  - Coefficients: 4, -7
  - Constant: ¾
- For 2x(x - 3y + 4):
  - Terms: x, -3y, 4
  - Coefficient: 2, 1 (in front of x)
  - Constant: 4