# Basics of Algebra

**Who introduced Algebra?**

Algebra was first discovered by a Muslim mathematician and astronomer named Muhammad ibn Musa al-Khwarizmi. This 9th-century mathematician is known as “The Father of Algebra”. The word “Algebra” is derived from his book Kitab Al-Jabr.

### **What is Algebra?**

Algebra is the branch of mathematics that uses numbers as constants and alphabets as variables to solve mathematical calculations. The alphabets are used to find unknown numbers through simple calculations like addition, subtraction, multiplication, and division. These calculations are done through algebraic equations.

For example,

a+12=0

a=0-12

a= -12

Therefore, the unknown number, which is the value of a is -12.

We use such algebraic equations in many areas, even unknowingly. The formula to find the area of a square. The formula is area (A) equals length (l) multiplied by the height (h):

A= lb

In algebraic expressions, when numbers and/or alphabets (known as factors) are multiplied together, they form terms or factors.

For example;

7a is a term.

It is the result of the multiplication of factors 7 and a.

Here, 7 is the coefficient of the variable a.

These terms are used to solve algebraic equations and sums.

**Addition and Subtraction:**

#### Addition and Subtraction of Like terms:

When two terms have the same variable with the same power, they are called Like terms. Here are some examples:

10x + 15x= 25x

Or,

*32a*^{2}* + 12a*^{2 }*= 20a*^{2}

When two terms have different variables, they are Unlike Terms. For example:

5x^{2 }+ 2y^{2} cannot be added because they are both, Unlike terms.

### Simplification:

*13x + 7x – 6x + 2a*

*(13x + 7x)- 6x + 2a*

*20x – 6x + 2a*

*14x + 2a*

**Multiplication**

For multiplication, the laws of Indices play a major part. Here are some examples:

#### Example 1:

*x*^{3}(*x*^{4} + 5*a*)

= *x*^{7} + 5*ax*^{3}

#### Example 2:

(*x* + 5)(*a* − 6)

= *x*(*a *− 6) + 5(*a* − 6)

= *ax* − 6*x* + 5*a* − 30

**Where do you use Algebra?**

Algebra is used in various fields of mathematics.

- Greatly used in medicine, accounting, and tech-related fields.
- Several professional fields like physics, engineering, programming, actuary use algebra for problem-solving
- Helps an individual to make their logical and analytical skills better.
- Used to solve complex problems and calculations
- Helps to improve critical thinking and logical reasoning.