expression

(noun)

An arrangement of symbols denoting values, operations performed on them, and grouping symbols (e.g., (2x+4)(2x+4)(2x+4)).

Related Terms

  • subset
  • superset
  • graph
  • set
  • equation
  • compound inequality
  • inequality
  • rational expression
  • polynomial
  • compound

(noun)

An arrangement of symbols denoting values, operations performed on them, and grouping symbols, e.g. (2x+4)2\displaystyle \frac{(2x+4)}{2}​2​​(2x+4)​​

Related Terms

  • subset
  • superset
  • graph
  • set
  • equation
  • compound inequality
  • inequality
  • rational expression
  • polynomial
  • compound

Examples of expression in the following topics:

  • Simplifying Exponential Expressions

    • Multiplying exponential expressions with the same base: am⋅an=am+na^m \cdot a^n = a^{m+n}a​m​​⋅a​n​​=a​m+n​​
    • Previously, we have applied these rules only to expressions involving integers.
    • The same rule applies to expressions with variables.
    • Now apply the rule for dividing exponential expressions with the same base:
    • To simplify the first part of the expression, apply the rule for multiplying two exponential expressions with the same base:
  • Simplifying, Multiplying, and Dividing Rational Expressions

    • Performing these operations on rational expressions often involves factoring polynomial expressions out of the numerator and denominator.
    • As a first example, consider the rational expression 3x3x\frac { 3x^3 }{ x }​x​​3x​3​​​​.
    • We follow the same rules to multiply two rational expressions together.
    • Dividing rational expressions follows the same rules as dividing fractions.
    • The same applies to dividing rational expressions; the first expression is multiplied by the reciprocal of the second.
  • Simplifying Radical Expressions

    • A radical expression that contains variables can often be simplified to a more basic expression, much as can expressions involving only integers.
    • Expressions that include roots are known as radical expressions.
    • A radical expression is said to be in simplified form if:
    • For the purposes of simplification, radical expressions containing variables are treated no differently from expressions containing integers.
    • This follows the same logic that we used above, when simplifying the radical expression with integers:
  • Adding and Subtracting Algebraic Expressions

    • Every algebraic expression is made up of one or more terms. 
    • Terms in these expressions are separated by the operators +++ or −-−.
    • For instance, in the expression x+5x + 5x+5, there are two terms; in the expression 2x22x^22x​2​​, there is only one term.
    • The same rules apply when an expression involves subtraction.
    • The expression therefore simplifies to:
  • Negative Exponents

    • This rule makes it possible to simplify expressions with negative exponents.
    • For example, consider the rule for multiplying two exponential expressions with the same base.
    • Note that the rule for raising an exponential expression to another exponent can be applied:
    • Recall that the rule for multiplying two exponential expressions with the same base can be applied.
    • Therefore, we can simplify the expression inside the parentheses:
  • Introduction to Radicals

    • Radical expressions yield roots and are the inverse of exponential expressions.
    • Mathematical expressions with roots are called radical expressions and can be easily recognized because they contain a radical symbol (\sqrt{}√).
    • Since roots are the inverse operation of exponentiation, they allow us to work backwards from the solution of an exponential expression to the number in the base of the expression.
    • In this expression, the symbol is known as the "radical," and the solution of 7 is called the "root."
    • Finding the value for a particular root can be much more difficult than solving an exponential expression. 
  • The Order of Operations

    • The order of operations is an approach to evaluating expressions that involve multiple arithmetic operations.
    • The order of operations is a way of evaluating expressions that involve more than one arithmetic operation.
    • For example, when faced with the expression 4+2⋅34+2\cdot 34+2⋅3, how do you proceed?
    • In order to be able to communicate using mathematical expressions, we must have an agreed-upon order of operations so that each expression is unambiguous.
    • This expression correctly simplifies to 9.
  • Rational Algebraic Expressions

    • When applying this strategy to rational expressions, first look at the denominators of the two rational expressions and see if they are the same.
    • This requires factoring algebraic expressions.
    • For example, consider the expression 2x2+42x^2 + 42x​2​​+4.
    • This expression therefore has two factors: 222 and (x2+2)(x^2 + 2)(x​2​​+2).
    • The rational expressions therefore become:
  • Equations and Inequalities

    • An equation states that two expressions are equal, while an inequality relates two different values.
    • An equation is a mathematical statement that asserts the equality of two expressions.
    • This is written by placing the expressions on either side of an equals sign (=), for example:
    • Equations often express relationships between given quantities—the knowns—and quantities yet to be determined—the unknowns.
    • The process of expressing the unknowns in terms of the knowns is called solving the equation.
  • Introduction to Exponents

    • For example, the expression b3b^3b​3​​ represents b⋅b⋅bb \cdot b \cdot bb⋅b⋅b.
    • Here, the exponent is 3, and the expression can be read in any of the following ways:
    • Now that we understand the basic idea, let's practice simplifying some exponential expressions.
    • Let's look at an exponential expression with 2 as the base and 3 as the exponent:
    • Let's look at another exponential expression, this time with 3 as the base and 5 as the exponent:
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