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 …

Binomial theorem primarily helps to find the expanded value of the algebraic expression of the form (x + y) n. Finding the value of (x + y) 2, (x + y) 3, (a + b + c) 2 is easy and can be obtained by …

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. …

Jan 8, 2026 · 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 …

The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. The larger the power is, the harder it is to expand expressions like this directly. But with the Binomial …

What is the Binomial Theorem for? The Binomial Theorem is a quick way (okay, it's a less slow way) of expanding (that is, of multiplying out) a binomial expression that has been raised to some (generally …

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: …

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.

Apr 27, 2025 · When we expand (x + y) n by multiplying, the result is called a binomial expansion, and it includes binomial coefficients. If we wanted to expand (x + y) 52, we might multiply (x + y) by itself …