Section 1.2: Expressions & Terms
An algebraic expression is a combination of numbers, variables, and operations. Expressions do not have an equal sign, unlike equations.
Key Vocabulary:
- Term – a number, variable, or product of numbers and variables (e.g., \( 3x \), \( -7 \), \( y^2 \)).
- Coefficient – the numerical factor of a term (e.g., 5 in \( 5x \)).
- Constant – a term without variables (e.g., 12).
- Expression – a sum or difference of terms (e.g., \( 2x + 3y - 7 \)).
Example 1
Identify the terms, coefficients, and constants in the expression: \( 4x + 7 - 3y \).
Terms: \( 4x \), \( 7 \), \( -3y \)
Coefficients: 4 (for \( 4x \)), -3 (for \( -3y \))
Constant: 7
Example 2
Write an expression for: "The product of 3 and a number \( n \), plus 5."
The product of 3 and \( n \) is \( 3n \).
Adding 5 gives the expression: \( 3n + 5 \).
Practice Problems
- List the terms, coefficients, and constant in \( 6x - 4y + 9 \).
- Translate into an expression: "Twice a number decreased by 7."
- Write the algebraic expression for: "The sum of a number and 12."
- Which part of the expression \( 5x + 2y - 11 \) is the constant?
- Write an expression for: "Four more than triple a number."