Quadratic Equations: A quadratic equation can be written in the standard form as ax 2 + bx + c = 0, where a, b, c are constants and x is the variable.In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions. Linear Equations: Linear equations help in representing the relationship between variables such as x, y, z, and are expressed in exponents of one degree.Given below are the different types of equations, based on the degree of the variable, where we apply the concept of algebra: Example: 5x 3 + 4x 2 + 7x + 2 = 0.Īn equation is a mathematical statement with an 'equal to' symbol between two algebraic expressions that have equal values. A polynomial is an expression consisting of variables (also called indeterminates), coefficients, and non-negative integer exponents of variables. Algebraic expressions are also known as polynomials. Further, the variables can be simple variables using alphabets like x, y, z or can have complex variables like x 2, x 3, x n, xy, x 2y, etc. Here 5 and 6 are fixed numbers and x is a variable. An example of an algebraic expression is 5x + 6. Algebraic ExpressionsĪn algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). Here, we have listed some of the important topics of algebra such as algebraic expressions and equations, sequence and series, exponents, logarithm, and sets. Any of the real-life problems can be classified into one of the branches of mathematics and can be solved using abstract algebra.Īlgebra is divided into numerous topics to help for a detailed study. All the other branches of algebra can be considered as the subset of universal algebra. Across these topics, universal algebra studies mathematical expressions and does not involve the study of models of algebra. Universal AlgebraĪll the other mathematical forms involving trigonometry, calculus, coordinate geometry involving algebraic expressions can be accounted as universal algebra. Abstract algebra finds numerous applications in computer sciences, physics, astronomy, and uses vector spaces to represent quantities. Group theory and ring theory are two important concepts of abstract algebra. Rings are a simple level of abstraction found by writing the addition and multiplication properties together. Abstract AlgebraĪbstract algebra deals with the use of abstract concepts like groups, rings, vectors rather than simple mathematical number systems. A general form of representation of a quadratic equation is ax 2 + bx + c = 0, and for a polynomial equation, it is ax n + bx n-1+ cx n-2+. Elementary algebra based on the degree of the variables, branches out into quadratic equations and polynomials. Linear equations are of the form, ax + b = c, ax + by + c = 0, ax + by + cz + d = 0. Based on the degree of the variable, the equations are called linear equations, quadratic equations, polynomials. In elementary algebra, simple variables like x, y, are represented in the form of an equation. Elementary AlgebraĮlementary algebra deals with solving the algebraic expressions for a viable answer. Forming a mathematical expression of the given problem statement is part of pre-algebra. It helps in transforming real-life problems into an algebraic expression in mathematics. The basic ways of presenting the unknown values as variables help to create mathematical expressions. Based on the use and the complexity of the expressions, algebra can be classified into various branches that are listed below: The complexity of algebra is simplified by the use of numerous algebraic expressions. Understanding algebra as a concept is more important than solving equations and finding the right answer, as it is useful in all the other topics of mathematics that you are going to learn in the future or you have already learned in the past. It is not just a mathematical concept, but a skill that all of us use in our daily life without even realizing it. One simple example of an expression in algebra is 2x + 4 = 8.Īlgebra deals with symbols and these symbols are related to each other with the help of operators. All the branches of mathematics such as trigonometry, calculus, and coordinate geometry, involve the use of algebra. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.
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