Binomial Theorem Calculator

The Binomial Theorem Calculator allows users to expand binomial expressions of the form (x + y)^n, providing details such as the expanded form, first and last terms, number of terms, Pascal’s Triangle coefficients, middle terms, and the sum of coefficients for exponents ranging from 0 to 10.

Use Our Binomial Theorem Calculator

Using the Binomial Theorem Calculator

This Binomial Theorem Calculator is designed to help you expand binomials and compute various properties of binomial expansions. By inputting your values and following the steps below, you can easily obtain the expanded form, term values, and coefficients.

Step-by-Step Guide

  1. Enter the Base Value (x):

    In the input field labeled Base Value (x), enter the numerical value for the first term of the binomial. This value is essential for calculating the expansion.

  2. Enter the Second Term (y):

    In the input field labeled Second Term (y), enter the numerical value for the second term of the binomial. Both the base value and this second term will be used throughout the calculations.

  3. Enter the Exponent (n):

    In the input field labeled Exponent (n), provide a whole number between 0 and 10. This exponent indicates how many times the binomial is multiplied by itself.

  4. View the Expanded Form:

    Once the values are entered, the calculator will provide the expanded form of the binomial expression. The formula (baseValue + secondTerm)^exponent will be used to expand your input into a polynomial expression.

  5. Find the First Term:

    The calculator will compute the value of the first term in the expansion, which is calculated as baseValue raised to the power of the exponent.

  6. Obtain the Last Term:

    The last term of the polynomial expansion, being the secondTerm to the power of the exponent, will also be displayed.

  7. Determine the Number of Terms:

    The calculator will show the total number of terms in the expanded form, which is always one more than the exponent.

  8. Get Pascal Triangle Coefficients:

    The coefficients from Pascal’s Triangle corresponding to the exponent are generated and shown in a list. These coefficients are pivotal in forming each term in the polynomial.

  9. Identify the Middle Term(s):

    The middle term(s) of the expansion, if applicable, are calculated based on the position in the polynomial and are displayed in this section.

  10. Sum of Coefficients:

    The sum of all coefficients in the expansion will be calculated. This is equivalent to 2 raised to the power of the exponent.

By following these steps, you’ll be able to fully explore the properties and terms of the binomial expansion using the Binomial Theorem Calculator.