Skip to main content
Back

College Algebra: Algebraic Expressions

Control buttons has been changed to "navigation" mode.
1/20
  • What is an algebraic expression?
    A combination of numbers and variables with math operations.
  • What is a variable in algebraic expressions?
    A letter representing any number; its value can vary and is usually a letter.
  • What is a coefficient?
    A number multiplying a variable; its value doesn't vary and is usually at the front.
  • What is a constant in algebraic expressions?
    A number without variables; its value doesn't vary and is usually at the end.
  • What symbol forms an equation when placed between expressions?
    The equal sign (=) forms an equation.
  • What does it mean to evaluate an algebraic expression?
    To substitute given values for variables and use PEMDAS to simplify.
  • What is the order of operations?
    Parentheses, Exponents, Multiply/Divide, Add/Subtract.
  • What is the difference between numerical and algebraic expressions?
    Numerical expressions have numbers and operations; algebraic expressions also include variables.
  • What does an exponent represent?
    Repeated multiplication of the base number.
  • Define the base and exponent in an expression like \(a^n\).
    Base is the number being multiplied; exponent is the number of times the base is multiplied.
  • How do you simplify algebraic expressions?
    By reducing the number of terms through combining like terms.
  • What are like terms?
    Terms with the same variables raised to the same powers.
  • What are the steps to simplify algebraic expressions?
    1) Distribute constants/variables through parentheses, 2) Group like terms, 3) Combine like terms.
  • What is a term in an algebraic expression?
    Parts of expressions separated by plus (+) or minus (-) signs.
  • How do you identify coefficients and constants in an expression like \(2x + 5\)?
    Coefficient is the number multiplying the variable (2), constant is the standalone number (5).
  • What should you do first when evaluating expressions with exponents?
    Evaluate the exponents before other operations.
  • What is the value of \(x^3\) called?
    It is called x cubed or x to the third power.
  • How do you evaluate the expression \(2y - x(3 + y)\) when given values for x and y?
    Substitute the values for x and y, then follow PEMDAS to simplify.
  • What is the purpose of distributing in simplifying expressions?
    To remove parentheses by multiplying the term outside the parentheses with each term inside.
  • What does the expression \(a \cdot a \cdot \ldots \cdot a\) represent?
    It represents a multiplied by itself n times, or a to the nth power.