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College Algebra: Algebraic Expressions

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  • What is an algebraic expression?
    A combination of numbers and variables with math operations.
  • Define a variable in algebraic expressions.
    A letter which represents any number.
  • What is a coefficient?
    A number multiplying a variable in an algebraic expression.
  • What is a constant?
    A number without variables in an algebraic expression.
  • Does the value of a numerical expression vary?
    No, numerical expressions have values that do not vary.
  • Does the value of an algebraic expression vary?
    Yes, algebraic expressions can vary depending on variable values.
  • What symbol forms an equation when placed between expressions?
    An equal sign (=) forms an equation.
  • What does it mean to evaluate an algebraic expression?
    To substitute given values for variables and calculate using PEMDAS.
  • What is the order of operations?
    Parentheses, Exponents, Multiply/Divide, Add/Subtract.
  • What do exponents represent?
    Repeated multiplication of the same base number.
  • In the expression \(a^n\), what does a represent?
    Base: the number being multiplied repeatedly.
  • In the expression \(a^n\), what does n represent?
    Exponent or power: the number of times the base is multiplied.
  • When simplifying algebraic expressions, what is a term?
    Parts of expressions separated by plus (+) or minus (−) signs.
  • What are like terms?
    Terms with the same variables raised to the same powers.
  • What are the three types of terms in expressions?
    Number only (constant), variable only, and number with variable.
  • What is the first step in simplifying algebraic expressions?
    Distribute constants or variables through parentheses.
  • What is the second step in simplifying algebraic expressions?
    Group like terms by writing them next to each other.
  • What is the third step in simplifying algebraic expressions?
    Combine like terms by adding or subtracting their coefficients.
  • Why must exponents be evaluated before other operations?
    Because exponents have higher priority in the order of operations.
  • How do you evaluate the expression \(2x+5\) when \(x=3\)?
    Substitute 3 for x: \(2(3)+5=11\).
  • What does the expression \(4x\) represent?
    A variable x multiplied by the coefficient 4.