In this blog, we will study the history of Algebra equations, and also, we study What are Algebra equations?

In mathematics, the branch of Algebra equations is as old as maths. The univariate equations over the rational coefficients have an ancient history. The father of mathematics is Archimedes and, the father of algebra is Al-Khwarizmi.

In 1637, René Descartes published La Geometries, invented the modern algebraic notation (use of alphabets to represent known and unknown numbers). In the mid-16th century, cubic and quadratic equations were introduced in mathematic.

## What are the Algebra equations?

Algebra equations are one of the most important branches of mathematics.

It is a set of equality of two expressions with Algebraic operations like addition, subtraction, multiplication, division, and raises to a power. In other words, Algebra equations or polynomial equation is an equation of the form

P=0

Where P is the polynomial with coefficients in the same field.

So, an algebraic equation is univariate which means it has one variable and a polynomial is multivariate. A polynomial equation is represented as

ax^n + bx^{n – 1} + … + gx + h = k

Here, a,b are the coefficients and n is the power of the variable x. For an algebraic equation the value of n=2

As a result, the algebra equation can be represented

ax^2+bx+h=0

For Example :

6x^2+9x=2x^2+4x-5,

6x^2+9x-2x^2-4x+5=0,

4x^2+5x+5=0

In other words, it’s just like a rural scale or balancing scale. On a balancing scale, we need to keep an equal amount of weight to keep either side of the scale balanced. So, if try to increase the weight on any one side then, it became imbalanced.

Likewise, algebra equations follow the same trend.
Also, Check more details on Algebraic expression.

The solution of algebra equations is the procedure of finding a number or set of numbers when it is substituted in place of a variable in an equation, reduced to identity.

Moreover, this Algebra is part of our daily routine. These algebra equations can be used to calculate the budgets, rates, profits and can help to make the prediction.

Few applications of algebra in real life are morning routine, business and finance management, sports, Cooking, logical thinking, health, and fitness.

## What is the different type of Algebra equations?

These algebraic equations are of 5 types, which can be differentiated by the position of variable, different types of grape, operation types, and functions used. In layman language, for every different type of input, the output will be different for all the types of equations.

• Monomial/polynomial algebra

Monomial equations are equations that consist of variable terms with whole-number exponents. All the polynomial equations are parts of algebraic equations but not all the algebraic equations are polynomial. In short, monomials have one term, binomial has two terms and more than one term is called polynomial (equations comprise of variable, constants, and coefficients)

ax+b=c (a≠0).
Moreover, Quadratic equation can be written as

ax^2+bx+c=0 (a≠0).

• Exponential equation

The exponential function is defined as an equation in which a variable occurs exponentially. It can be classified as exponential growth for positive coefficients and exponential decay for negative coefficients. Exponential decay equations are used in radioactive decay and exponential growth equations are used in describing the population and financial concepts. This can be represented as

For example : f(x) = a^x , where a > 0 and a ≠ 1

• Logarithmic equation

The logarithmic equation is an equation involving the logarithm of an expression having variables. As a result, the logarithmic function can be represented as inverse of the exponential function represented as \log_ex .The logarithmic ‘e’ is called a natural logarithm.
For example : \frac{1}{k}\log_2 c(f)\;

• Rational Equation

A rational equation defined as an algebraic equation containing at least one fraction whose numerator and denominator represented as P(x)/Q(x) where P(x) and Q(x) are both polynomials. These fractions can be on one side or on both the side of algebra equations to reduce it to a common denominator.

For example : \frac{x-1}{x-2}=\frac{3}{2};

• Trigonometric equation

An equation that involves the trigonometric function of a variable is termed a trigonometric equation and it can be expressed as sin, cos, tan, cosec, sec, and a cot and involves a ratio of unknown angles.

For example : Y=\sin x

After that, We will focus on other concepts of Algebra which include the basics of Algebra equations, formulas, and examples.

## Few examples to show the Algebra equation with solutions

Problem 1: 2 kg of sugar and 4 kg of flour are needed to be mixed to make 1 kg of Cake, and 1 kg of sugar and 3 kg of flour is needed to be mixed to make 1 kg of pudding.
How many kg of each type of sweet was manufactured if it is known that 300 kg of sugar and 200 kg of flour were used?

### Problem 1 Solution

Solution: Let us assume that x be the kg of Cake and y be the kg of Pudding.

So, let’s form the algebraic equations now
2x+4y=300        (equation 1)
1x+3y=200         (equation 2)

So, we will be solving this linear equation 1

x=\frac{300-4y}{2} is equation 3

Putting equation 3 in equation 2

1 \frac{300-4y}{2} +3y=200

150-2y+3y=200

y=200-150

Therefore, y=50

Putting the value of y in equation 3

Therefore, x=50

As a result, the value of x = 50 and y=50.

Problem 2: Solve 2x^2-x-28=0

### Problem 2 Solution

2x^2-x-28=0

2x^2-8x+7x-28=0 2x(x-4) +7(x-4) =0

(x-4) (2x+7) =0

As a result,  x=4 & \frac {-7}{2}

Problem 3: Solve 7x-5=5x-3

### Problem 3 Solution

Solution:
Given equation is 7x-5=5x-3

Taking all the line terms on one side and other on the other side

7x-5x=5-3

2x=2
Therefore, x=1
As a result, the value comes out to be x=1.

## Difference Between Algebraic expressions and algebra equations

So, the question arises what is the difference between the algebraic expression and equation?

Here is the difference between them

Algebraic Expression

-It comprises numbers and variables with operation symbols.
– We simplify an expression
-An expression doesn’t have any relation symbol.
-For example 4x+3y+6

Algebraic Equation

-Two expressions joined by an equal sign.
-We solve an equation
-An equation has a relation symbol.
-For example : 2x-3=0

To sum up, check out our Blogging for Algebraic expression for more information on algebra and Algebra in Maths to learn the basics of algebra to improving your knowledge to solve any problem easily. Do comment and let us know your opinion on it.