What is the Binomial Theorem?

A binomial is a mathematical expression involving two unlike terms connected by plus or minus signs. For example, x + 5 is a binomial which has two terms x and 5. Binomial theorem describes the process to find the expanded value of the algebraic expression involving two variables which can be in the form (x + y) raised to the power n. Here n is called the exponent which indicates how many times an expression is multiplied. The value of an expression with a smaller value of exponent can be obtained by simple algebraic multiplication for a number of times based on the exponent value. But to find the expanded form of an algebraic expression having a higher exponent value, a rule has to be followed which is known as a binomial theorem. The exponent value of this binomial theorem expansion can be any integer including a negative number or a fraction. 

The binomial theorem is the principle for the expansion of a binomial expression with an exponent. As per the binomial theorem, a binomial in the form (x + y) having a non-negative exponent, can be expanded into a sum of different terms. The theorem states that the expanded form of the expression will be in the form of the sum of different terms involving variables x and y with the variables having individual exponent values. Each term in a binomial expanded form has a numeric value attached to the variables which are called a coefficient. For example, in the binomial expression 3x-2, the coefficient of x is 3.

Properties of Binomial Expansion

Some of the properties of binomial expansion are:

  • The expanded form of a binomial expression contains one term more than the number given as the power on the binomial. 
  • The sum of exponents of each term in the expanded form is equal to the power of the binomial.

Maths Online Classes

In the present scenario, the learning institutions have adapted themselves to the use of online platforms to provide learning to students. Various institutes are offering facilities to students for joining online classes to supplement their studies in an effective way. The online classes provide students and teachers the opportunity to interact through digital applications without being physically present at the same place. The learning management apps ensure user-friendly access to the online classes by students and teachers. They can make effective use of the digital tools and applications for learning in a convenient and interactive manner like traditional classroom sessions. The audio and video facilities, the online assignments, and tracking the results help students to go through a structured way of learning. 

Math online classes are structured in a way that helps students to develop conceptual clarity on the subject and confidence to handle mathematical problems. The online learning platforms use various learning apps that give students wide exposure to relevant topics. The students get to learn a variety of topics relevant to their requirements and receive guidance from teachers. The students are allowed to learn and apply different problem-solving techniques while handling various assignments. Online math classes allow students to learn in a relaxed and flexible environment, without the hassles of traveling, time constraints, and other distractions. 

The online classes also offer counseling sessions for students to guide them on the selection of suitable career paths. The online classes allow effective interaction between teachers and students that helps to resolve any doubts and work towards self-improvement. Online math classes use various application-based methods to make the learning enjoyable and effective for students of any age group. The focus of online math classes is to train the students in practice-based learning through solving various types of assignments. This mode of learning is very essential for students of mathematics and develops the analytical abilities that help them to handle any complex problem with confidence.

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