In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

That pattern is summed up by the Binomial Theorem: Don't worry ... it will all be explained! And you will learn lots of cool math symbols along the way. First, a quick summary of Exponents. An exponent …

The binomial theorem formula helps in the expansion of a binomial raised to a certain power. Let us understand the binomial theorem formula and its application in the following sections.

Apr 27, 2025 · A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and …

Oct 18, 2025 · The binomial theorem is a mathematical formula that gives the expansion of the binomial expression of the form (a + b)n, where a and b are any numbers and n is a non-negative integer. …

Nov 19, 2025 · Binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers (a + b) may be expressed as the sum of n + 1 terms. The theorem is useful in algebra …

What is the formula for the Binomial Theorem? What is it used for? How can you remember the formula when you need to use it? Learn here!

However, there is another, much more important (and provable) pattern that can be exploited to produce the numbers on any single row even faster, and without reference to any other rows. This elegant …

The binomial theorem is used to expand polynomials of the form (x + y) n into a sum of terms of the form ax b y c, where a is a positive integer coefficient and b and c are non-negative integers that sum to n.

There are a number of different ways to prove the Binomial Theorem, for example by a straightforward application of mathematical induction. The Binomial Theorem also has a nice combinatorial proof: