https://mathmonks.com › binomial-theorem

The binomial theorem is a formula for expanding binomial expressions of the form (x + y) n, where ‘x’ and ‘y’ are real numbers and n is a positive integer. The simplest binomial expression x + y with two unlike terms, ‘x’ and ‘y’, has its exponent 0, which gives a value of 1 (x + y) 0 = 1

https://www.cuemath.com › algebra › binomial-theorem

The binomial theorem states the principle for expanding the algebraic expression (x + y) n and expresses it as a sum of the terms involving individual exponents of variables x and y. Each term in a binomial expansion is associated with a numeric value which is called coefficient.

https://www.geeksforgeeks.org › binomial-theorem

The Binomial Theorem provides a method to expand expressions that are raised to a power such as the (x + y)n. It is a crucial concept in algebra, particularly useful for expanding the polynomials and solving combinatorial problems. In this chapter, students learn to apply the Binomial Theorem to simplify and solve the various algebraic problems. Bi

https://en.wikipedia.org › wiki › Binomial_theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial ( x + y ) n into a sum involving terms of the form ax b y c , where the exponents b and c are nonnegative integers with b + c = n , and the coefficient a ...

https://math.libretexts.org › Bookshelves › Algebra › Algebra_and_Trigonometry_1e_(OpenStax...

THE BINOMIAL THEOREM. The Binomial Theorem is a formula that can be used to expand any binomial. \[ {(x+y)}^n = \sum_{k=0}^{n}\dbinom{n}{k}x^{n−k}y^k = x^n+\dbinom{n}{1}x^{n−1}y+\dbinom{n}{2}x^{n−2}y^2+...+\dbinom{n}{n−1}xy^{n−1}+y^n \]

https://www.storyofmathematics.com › binomial-theorem

The Binomial Theorem explains how to expand an expression raised to any finite power. This theorem has applications in algebra, probability, and other fields.

https://math.libretexts.org › Bookshelves › Algebra › Intermediate_Algebra_1e_(OpenStax) › 12...

Example \(\PageIndex{5}\) Use the Binomial Theorem to expand \((p+q)^{4}\). Solution: We identify the \(a\) and \(b\) of the pattern. Figure 12.4.11. In our pattern, \(a=p\) and \(b=q\). We use the Binomial Theorem.