Algebra Flashcards: The Distributive Property, Terms, and Factoring

Vocabulary flashcards covering the Distributive Property, expanding, terms, like and unlike terms, coefficients, and factoring based on the lecture notes.

Distributive Property of Multiplication over Addition

The property stating that for all real numbers $a$, $b$, and $c$, $c(a + b) = ca + cb$.

Expanding

The process of using the Distributive Property to rewrite a product like $c(a + b)$ as a sum of terms $ca + cb$, which has the effect of removing parentheses.

Distributive Property of Multiplication over Subtraction

The property stating that for all real numbers $a$, $b$, and $c$, $c(a - b) = ca - cb$.

Term

Either a single number or a variable, or a product of numbers and variables, separated by addition in an algebraic expression.

Like Terms

Terms that contain the same variables raised to the same powers, such as $3t$ and $40t$, or $y^2$ and $-19y^2$.

Unlike Terms

Terms that contain different variables or the same variables raised to different powers, such as $5t$ and $16t^2$, or $37x^3$ and $y^3$.

Coefficient

A number that is a factor in a term; for example, $-8$ is the coefficient of $k^2n$ in the term $-8k^2n$.

Factoring

The process of rewriting $ac + bc$ as $(a + b)c$, which changes addition into multiplication, introduces parentheses, and undoes expansion.