What is elementary algebra?
Elementary algebra is a branch of mathematics that deals with real numbers and the relationships between them. It is a fundamental subject in most fields of further math and statistics, as well as the natural sciences, computer science, and economics. It is also an important component of writing, which has been a central part of the development of many civilizations.
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Variables are mathematical symbols used to represent quantities such as x, a, n, and y. Using these symbols allows general relationships to be formally expressed and simplified, which is why they are a popular tool in algebra. These symbols are based on the letters of the alphabet and were first introduced in the late sixteenth century by French mathematician Francois Viete.
In addition, algebraic symbols are sometimes used to represent complex numbers and negative numbers. Unlike traditional arithmetic, algebra uses the geometric representation of numbers to represent these types of quantities. These quantities are often represented by a straight line that is infinite in both directions. The length of the line is a unit, and positive and negative real numbers extend to the right and left of the line.
Commonly, expressions involving these quantities are written in a form that is known as standard form, which uses the same rules for expressing a number or expression as those that are followed when writing an equation. This is an important part of the study of mathematics and is one of the main differences between algebra and arithmetic.
Polynomials are expressions built up from real and complex numbers by combining them in the three basic arithmetic operations, adding, subtracting, and multiplying. In addition to these arithmetic operations, polynomials can be combined according to the distributive law and commutative and associative laws. Combining polynomials in this way makes it easier to simplify and understand expressions that contain them, and several symbolic algebra programs make this work as easy as typing the expressions into a computer.
The commutative and associative laws for addition and multiplication are especially useful in the construction of expressions involving polynomials. These laws can help you avoid repeating the same terms in a product, so that you end up with a shorter term.
Another important part of the study of algebra is the use of exponents. These are the numerical powers of a base number, usually a, but can be anything from 0 to 1. When you multiply an exponent, you add that power to the original base. In addition, you can also add a multiplicative factor to the base number and get another exponent.
These exponents are a vital part of the study of algebra and are essential for understanding more advanced concepts that come on to calculus. They allow you to write polynomials, monomials, and rational expressions in a simpler manner.
Similarly, you can calculate the values of polynomials and monomials and evaluate them by calculating the square root or finding their absolute value. You can also use these techniques to solve quadratic equations and systems of linear equations.