Form a Simple and Complex Algebra Equation

 An algebraic equation is a mathematical statement in which two expressions are set equal to each other. An algebraic equation usually has a variable, coefficients, and constants. Algebra is a branch of mathematics concerned with symbols and the operations that may be applied to them. Variables are symbols that do not have predetermined values. In our daily lives, we regularly come with certain values that change. The need to articulate these changing values, on the other hand, remains constant. Variable symbols such as x, y, z, p, and q are often used in algebra to denote these values. To ascertain the values, these symbols are subjected to various mathematical operations such as addition, subtraction, multiplication, and division.

Algebra Equation:

An algebraic equation is a Mathematical statement that contains two equal algebraic expressions. The general form of an algebraic equation is A = 0 or A = B, where A and B are polynomials. Multivariate algebraic equations have more than one variable, whereas univariate algebraic equations have only one. An algebraic equation’s equilibrium is established. This means that the right and left sides of the equation will be equal.

Basic Rule of Algebra Equation

Some of the basic rules of the algebra for some variables, P, Q and R are as given below,

The Commutative Property of Addition: P + Q = Q + P

Commutative Property of Multiplication: P × Q = Q × P

Associative Property of Addition: P + (Q + R) = ( P + Q ) + R

Associative Property of Multiplication: P × ( Q × R ) = ( P × Q ) × R

Distributive Property: P × ( Q + R ) = ( P × Q ) + (P × R ), or, P × ( Q – R ) = ( P × Q ) – ( P × R )

Reciprocal: Reciprocal of P = 1/P

Additive Identity Property: P + 0 = 0 + P = P

Multiplicative Identity Property: P × 1 = 1 × P = P

Additive Inverse: P + (-P) = 0

Type of Algebraic Equation

Different forms of algebraic equations exist. Some algebraic equations include:

•  The Polynomial Equations
• The Quadratic Equations
• The Cubic Equations
• The Rational polynomial Equations
• The Trigonometric Equations

Algebraic Operation

• Addition, subtraction, multiplication, and division are the four basic processes studied in algebra.
• In algebra, the addition operation is performed by separating two or more equations with a plus (+) symbol.
• In algebra, the subtraction operation is performed by separating two or more equations with a negative (-) sign.
• Multiplication: In algebra, a multiplication () sign separates two or more equations for the multiplication operation.
• In algebra, the division operation is performed by separating two or more equations with a “/” symbol.

Simple Algebra Equation:

A simple algebra can be understood when any algebraic equation with elementary mathematical operations that use both constants and single variables, such as addition and subtraction are termed as simple algebra equations. This equation can be homogenous and monomial i.e., contain a single variable.

To form any simple algebra equation from scratch

• Read and understand the problem,
• Take unknown quantity a variable and write a simple equation with variable and constant,
• Use appropriate calculation to find variable 

Example of simple algebra equation:

7x – 14 = 0, here we can use simple calculation to find the value of x and the value of x here is 2.

Complex Algebraic Equation:

A Complex algebra can be understood when any algebraic equation with elementary mathematical operations that use both constants and single variables, such as addition and subtraction are termed as simple algebra equations. This equation can be heterogeneous and multinomial i.e., contain a single variable.

To form any Complex Algebra Equation from scratch

• Read and understand the problem,
• Take unknown quantity as some variable and write a complex equation with variable and constant by using multiplication division etc,
•  Use appropriate calculation to find variable 

Example of simple algebra equation:

X³ + y³ – 3x²y – 3xy² = 0, here we can use complex calculations to find the value of x and y .

Conclusion: 

An algebraic equation is one in which two algebraic expressions are connected by the equal sign. Algebra equations are polynomial equations. One-step, two-step, and multi-step algebraic equations are all possible. Based on the degree, algebra equations are classed as linear, quadratic, cubic, and higher-order equations.