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 - 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 - 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 are algebra expressions with only two terms, such as x + 1, y - 5 or 4*x. C
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.
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.
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.
See Cartesian Plane
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.
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
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
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.
A function is an algebra equation in which there are two variables such as y = 2*x + 3....
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