Algebra

Algebra - Algebra is simply doing arithmetic with at least one number replaced by a letter, which is referred to as an unknown and can be either a variable or a constant. For example, you know how to do 3 + 2 = 5. This is arithmetic. If we replace 2 with x we have 3 + x = 5. We know just from looking at this that x = 2. Algebra is simply a set of rules to find out the value of x.

Algebra Equations

Algebra Equations - An arithmetic or algebra equation is simply an arithmetic or algebra expression with an = sign. For example the arithmetic equations 3 + 2 = 5 or 3 * 5 = 15 and the algebra equations 3 + x =5 or 3 * x = 15.

Algebra Expressions

Algebra Expressions - An arithmetic expression is a sequence of numbers and operations such as 3 + 2 or 3 * 5 or 6 / 3. (Note that we DO NOT use the symbol x to indicate multiplication because in algebra x is frequently used as an unknown or variable). An algebra expression is a sequence of numbers, letters and operations such as 3+x or 3 * x or x / 3. B

Binomials

Binomials - Binomials are algebra expressions with only two terms, such as x + 1, y - 5 or 4*x. C

Cartesian Coordinates

Cartesian Coordinates, sometimes called Rectangular Coordinates, are named after the French mathematician Rene' Descartes who developed this system of graphically representing any point uniquely in a plane by two numbers, usually x and y. The coordinates consist of two lines intersecting perpendicular to one another. These lines are referred to as the x-axis and the y-axis. Any point on the rectangular plane defined by the two lines can be represented by a combination of distances along the x and y axes.

Cartesian Plane

A plane is a two dimensional surface which has infinite width, infinite length and zero thickness. The plane created by the x and y axes of the Cartesian Coordinates is referred to as the Cartesian Plane.

Completing the Square

One of the four methods of solving Quadratic Equations. Completing the Square is a method in which terms are added to both sides of the general Quadratic Equation ax2 + bx + c = 0 where a, b and c are constants, such that the resulting expression on the left side is a perfect square of a given binomial.

Constants

As discussed previously, Algebra involves doing arithmetic with numbers and letters (for example 3 + x = 5) The letters are referred to as unknowns. Sometimes the letters can take on a variety of values and are called variables. Other times the letters have an unknown but fixed value and are called constants.

Coordinate Plane

See Cartesian Plane

Cube Root

The cube root of a given number is the unique number that when raised to the 3rd power (multiplied by itself 3 times) will equal the original given number.

D

Domain

The domain of a function consists of all real values of x that yield real values of y when the domain values of x are substituted for xin the function. E

Exponent

In arithmetic an exponent is represented by a base number with a super scripted number such as 23. The base number in this case is 2 and the exponent is 3. The exponent is the number of times the base is multiplied by itself. In our example 23 = 2 * 2 * 2 = 8. In Algebra, the base is usually an unknown or a variable such as x. In this case our equation would become x3 = x * x * x. F

FOIL Method

The FOIL Method is an acronym that helps us remember how to multiply together two binomials. For instance the (x + 2) * (x + 3). The FOIL Method consists of multiplying the First two terms (x*x), then multiplying the Outermost terms (x*3), then multiplying the I>nnermost two terms (2*x), then multiplying the Last two terms (2*3) and finally adding all the product together. The result is the following: (x + 2) * (x + 3) = x2 + 3*x + 2*x + 2*3 which can be combined to give x2 + 5*x + 6.

Function

A function is an algebra equation in which there are two variables such as y = 2*x + 3....