Algebraic Simplification and Polynomial Operations

Vocabulary practice flashcards covering rules, definitions, and step-by-step methods for simplifying algebraic expressions, multiplying binomials, finding rectangle area and perimeter, and using FOIL and Box methods.

Like Terms

Terms within an algebraic expression that have the exact same variable letter and exponent combination.

Combining Like Terms (Linear Expression)

The process of grouping and adding or subtracting terms with matching variables and constants; for example, simplifying $5x + 2 - 8x + 10$ results in $-3x + 12$.

Distributive Property (Monomial by Binomial)

The operation of multiplying the outside term across every term inside parentheses; for example, simplifying $5x(8x + 10)$ yields $40x^2 + 50x$.

Multiplying Binomials

The process of multiplying two binomials using FOIL or the Box Method; for example, expanding $(5x + 2)(8x + 10)$ yields $40x^2 + 50x + 16x + 20$, which simplifies to $40x^2 + 66x + 20$.

Squaring a Binomial

The method of evaluating a squared binomial by first expanding it into two identical binomial factors—such as rewriting $(5x + 2)^2$ as $(5x + 2)(5x + 2)$—and then using FOIL or the Box Method to simplify to $25x^2 + 20x + 4$.

Subtracting Binomial Expressions

The procedure of distributing a $-1$ to every term inside the second set of parentheses and then combining like terms; for example, $(5x + 2) - (8x + 10)$ becomes $5x + 2 - 8x - 10$, simplifying to $-3x - 8$.

Dual Monomial-Binomial Distribution

An expression simplification where each outside term is distributed to its respective parentheses—such as distributing $2x$ to the $1^{\text{st}}$ set and $-4$ to the $2^{\text{nd}}$ set in $2x(5x + 2) - 4(8x + 10)$—producing $10x^2 + 4x - 32x - 40$, which simplifies to $10x^2 - 28x - 40$.

Perimeter of a Rectangle

The sum of all four boundary sides of a rectangle, calculated using the formula $P = a + b + c + d$.

Area of a Rectangle

The two-dimensional space enclosed by a rectangle, calculated by multiplying the length times width.

Adding Binomial Expressions

The simplification procedure of removing the parentheses and combining like terms directly; for example, $(5x + 2) + (-8x + 10)$ simplifies to $-3x + 12$.

Converting Factored Form to Standard Form

The process of using FOIL or the Box Method to multiply binomial factors such as $f(x) = (2x - 3)(x + 10)$ into standard polynomial form.

Box Method

A visual technique for multiplying polynomials where terms are written along the top and side of a grid, the cells are filled by multiplication, and diagonal like terms are combined by addition or subtraction.

FOIL Method

An acronym and procedure for multiplying two binomials by multiplying the First terms, Outside terms, Inside terms, and Last terms, followed by adding or subtracting to combine like terms.