Algebra its uses, properties and examples

History

Algebraic history is diverse and rich. The word "algebra" derives from the word "al-jabr." Al-jabr is an Arabic word that appears in the title of the Dissertation Al-Kitab al-muhtasar fi hisab al-gabr wa-l-muqabala written down by Al-Kwarizmi in 820. Al-Kwarizmi is the father of algebra. The efforts of multiple mathematicians from different cultures and time periods are demonstrated by the history of algebra, each building upon the work of their predecessors to shape the discipline we recognize today. Basically, algebra is everywhere, and it helps people to solve all types of questions. Still, people find new methods and exciting things in the world of algebra.

Definition

Algebra is a branch of mathematics in which we solve mathematical problems and enable the derivation of unknown quantities. In other words, algebra uses symbols and rules to solve different types of equations and research the relationship between these variables. It entails using letters to represent unknown values and using some arithmetic and mathematical symbols to execute different procedures on these symbols.

Algebra provides a powerful tool for resolving different types of mathematical problems. Variables, constants, expressions, linear equations, quadratic equations, and polynomials are the basic terms of algebra.

Uses of Algebra

Overall, algebra gives a toolkit for describing relationships, solving real-world practical problems, and modeling relationships between values in different fields. Algebraic techniques are necessary for solving a large range of mathematical questions.

Several are the important uses of algebra

• Programming and computer graphics
• Medicine Research and genetics
• Data Analysis and Statistics
• Spacecraft Trajectory Planning
• Cryptography
• Economics and Finance
• Astronomy and Geometry
• Science and Engineering

Basic Rules and Properties of Algebra

Commutative Property 

1. For Addition: x + y = y + x
2. For Multiplication: x × y = y × x

Associative Property 

1. For Addition: x + (y + z) = (x + y) + z
2. For Multiplication: x × (y × z) = (x × y) × z

Distributive Property

1. For Multiplication over Addition: x × (y + z) = (x × y) + (x × z)
2. For Multiplication over Subtraction: x × (y - z) = (x × y) - (x × z)

Reciprocal

1. Reciprocal of x = 1/x

Identity Property

1. Additive: x + 0 = 0 + x = x
2. Multiplicative: y × 1 = 1 × y = y

Additive Inverse

1. The additive inverse of x: x + (-x) = 0

Examples

There are some basic examples of algebra.

1- In first example we are going to find the value of a:

2- In second example we are going to find the value of b:

3- In third example we are going to find the value of c:

4- In fourth and last example we are going to find the value of d: