What is the formula for expansion?

The binomial expansion formula involves binomial coefficients which are of the form (nk) (or) nCk n C k and it is calculated using the formula, (nk) =n! / [(n – k)! k!]. The binomial expansion formula is also known as the binomial theorem.

What is the general formula of binomial expansion?

The general term of the binomial expansion is Tr+1=nCrxn−ryr T r + 1 = n C r x n − r y r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.

How do you write an expanded polynomial in standard form?

The steps to writing the polynomials in standard form are:

  1. Write the terms.
  2. Group all the like terms.
  3. Find the exponent.
  4. Write the term with the highest exponent first.
  5. Write the rest of the terms with lower exponents in descending order.
  6. Write the constant term (a number with no variable) in the end.

How do you expand XY N?

For any positive integer n, the expansion of (x + y)n is C(n, 0)xn + C(n, 1)xn-1y + C(n, 2)xn-2y2 + + C(n, n – 1)xyn-1 + C(n, n)yn. Each term r in the expansion of (x + y)n is given by C(n, r – 1)xn-(r-1)yr-1. Example: Write out the expansion of (x + y)7.

How do you write a polynomial equation?

To write a polynomial equation, we follow these steps:

  1. Write the roots as factors, changing the signs and putting each factor in parentheses.
  2. Multiply pairs of roots together using a box to organize the multiplication.
  3. Make sure that each factor has been multiplied by every other factor, and.

What is polynomial equation in differential equation?

The differential equation must be a polynomial equation in derivatives for the degree to be defined. Example 1: d 4 y d x 4 + ( d 2 y d x 2 ) 2 – 3 d y d x + y = 9. Here, the exponent of the highest order derivative is one and the given differential equation is a polynomial equation in derivatives.