Algebraic Properties and Expressions Flashcards

Study Notes

Algebraic Properties and Expressions

Exponent: Indicates how many times to multiply the base by itself. Example: In 2^3, the exponent is 3, so 2 * 2 * 2 = 8.
Base: The main number in an exponential expression that is raised to a power. Example: In 2^3, the base is 2.
Exponential Expression: Contains an exponent and may include variables. Example: 4x^3 translates to 4 * x * x * x.
PEMDAS: Acronym for the order of operations:
- P: Parentheses
- E: Exponent
- MD: Multiply/Divide
- AS: Add/Subtract
Variables: Symbols (often lowercase, italicized) representing unknown or changeable values. Example: In 4x - 5y = 9, x and y are variables.
Terms: Components of algebraic expressions separated by + or - signs, which may include numbers, variables, or both. Example: In 5x^2 + 2x + 7, the terms are 5x^2, 2x, and 7.
Algebraic Expressions: Mathematical phrases that include one or more variables. A numerical expression contains no variables. Example: p - 4 is an algebraic expression with variable p.
Coefficients: Numbers that multiply the variables in a term. Example: In -7x, -7 is the coefficient; in y, the coefficient is 1.
Like Terms: Terms that share the same variable and exponent. Example: 5ab and -22ab are like terms; 8x^2 and 6x are not due to differing exponents.
Distributive Property: Allows multiplication over addition or subtraction; if a, b, and c are expressions, then a(b + c) = ab + ac. Example: 5(x + 2) = 5x + 10.
Radical Expressions: Math expressions containing radical signs (sqrt) indicating roots.
Radicands: The numbers found under the radical sign in radical expressions.
Radical: Symbol (√) representing square roots or (ⁿ√) for nth roots. Example: √3 indicates the square root of 3, approximately equal to 1.732.