Algebraic Basics and PEMDAS

Vocabulary terms and foundational concepts regarding the order of operations and basic algebraic expressions.

PEMDAS

The acronym for the Order of Operations consisting of: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

P (in PEMDAS)

Parentheses, represented by grouping symbols such as $(-)$, $[-]$, or $\{-\}$.

E (in PEMDAS)

Exponents.

M (in PEMDAS)

Multiplication.

D (in PEMDAS)

Division.

A (in PEMDAS)

Adition.

S (in PEMDAS)

Substraction.

Algebraic Expression

A statement involving at least two different numbers or variables and at least one operation.

Terms

Individual components of an expression; for example, the expression $x^4 - 2xy^2 + 3y^4 - 5$ is composed of four identified terms: $T_1$, $T_2$, $T_3$, and $T_4$.

Variable

A leter used in an algebraic expression.

Substitute

The process of replacing variables with specific numbers to find a numerical value, such as replacing $x$ with $5$ and $y$ with $10$ in the expression $2x + 4xy^2$.

Numerical Value Calculation (Example)

In the expression $2x + 4xy^2$ where $x = 5$ and $y = 10$, the substitution results in $2 \cdot 5 + 4 \cdot 5 \cdot 10^2 = 10 + 20 \cdot 100 = 2010$.