# Algebraic Expressions

# Algebra Terms

## Get down with the lingo

### Associative Property

The rule that states that the sum and product of 3 or more numbers are the same no matter how you group them. For example: (*a*+

*b*) +

*c*=

*a*+ (

*b*+

*c*) and (

*a*×

*b*) ×

*c*=

*a*× (

*b*×

*c*).

### Algebraic Expression

An expression that contains one or more terms and operations to be combined. Each term contains variable(s), constant(s), or products of variables and constants. Once you have simplified an expression, it is considered "post-op." Might be nice if you swung by for a visit, or maybe brought it a stuffed teddy bear### Area

The amount of space inside the boundary of a closed shape. As in, "there is*x*room to fit all the aliens inside Area 51."

**Circle**

A closed plane figure wherein points on the boundary are equidistant from the fixed center. More importantly, it is the shape of a pizza pie.### Coefficient

### Commutative Property

The rule that states that changing the order of the operands, or the numbers on which an operation is performed, does not change the answer. Addition and multiplication on numbers are commutative properties, whereas division is not. You hear that, division? We want you off our commutative property, or we are calling the authorities.### Constant

### Dependent Variable

A variable in a function that changes due to the independent variable. It is very flexible. You should see what it can do with its legs.### Distributive Property

The rule where multiplication of numbers distributes over addition and subtraction: (*b*±

*c*) =

*ab*±

*ac*. Start distributin' the news.

### Equation

An expression that states the equation of two algebraic expressions. Equations: bringing expressions together since 1931.### Equivalent Equations

Two different equations that have the same solution(s). However, one of them is bound to argue that he thought of it first.### Equivalent Expression

Two different expressions in which the values obtained after substituting variables are equal. They must have gotten such strong values from their parents.### Exponent

An item that denotes the number of times the base number is to be multiplied. It is small and raised, like the hand of an Oompa-Loompa who has a question.### Factoring

The act of breaking up an algebraic expression into two or more expressions that can be multiplied together to get the original expression. It is worlds of fun to pull out factors. In fact, you haven't lived until you have been to a factor pull.### Factorization

The act of expressing a number as the product of its factors. Factorization is not unique. Ooh, that was kinda harsh. For example, 24 can be factorized as 8 × 3 and 6 × 4.### FOIL

A way to memorize the order in which you multiply together two binomials. Multiply the first terms, then the outer terms, then the inner terms, and finally, the last terms. Hey—that spells "FOIL!" Oh. Not a coincidence. Got it.### Formula

An expression used to determine the relationship between two or more variables. It can also be gleaned by checking its status on Facebook.### Function

A relation between two sets, input and output, such that for each input, there is exactly one output. A function is commonly denoted as*f*(

*x*), where

*x*is the input and

*f*(

*x*) is the output. Not to be confused with FX, which outputs only edgy and original programming.

### Greatest Common Factor (GCF)

The largest positive integer that evenly divides, with no remainder, two or more nonzero numbers. For example, the gcf of 18 and 24 is 6. It is also known as the greatest common divisor or highest common factor. Or, in certain parts of Mexico, as "El Factro Comme."### Independent Variable

A variable in a function that assumes values freely or independently. That is because they are American variables.### Like Terms

Two terms that have the same variables raised to the same exponent. Like terms may have different coefficients. We give them permission.### Parallelogram

A four-sided, closed shape with straight lines and two pairs of opposite sides that are parallel. You can send someone a parallelogram for his or her birthday, but it is not as entertaining as a sing-o-gram.### Perimeter

The length of the boundary of a closed shape. If the boundary is a light, bluish-purple and you can only see it out of the corner of your eye, it is a peripheral periwinkle perimeter. Just in case that ever comes up.### Rectangle

A parallelogram with all angles equal to 90°. More importantly, it is the shape of a rectangular pizza.### Solution

The value(s) of variable(s) that satisfy an equation or inequality…and allows you to move onto the next problem. Huzzah.### Square

A parallelogram with all angles equal to 90° and all sides equal. Read: glorified rectangle.### Trapezoid

A four-sided, closed shape with straight lines and only one pair of opposite sides equal. The best of all shapes, because of how much fun it is to say "zoid."### Triangle

A three-sided, closed shape with straight lines. Try back tomorrow at 9 am—it may be open then.### Variable

A value that changes. A variable is commonly represented by the letters*x*,

*y*, or

*z*, which can get confusing if you ever confront a word problem that involves someone driving along Zyzzyx Road.