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

Let us multiply a+b by itself using Polynomial Multiplication : (a+b) (a+b) = a2 + 2ab + b2. Now take that result and multiply by a+b again: (a 2 + 2ab + b 2) (a+b) = a3 + 3a2b + 3ab2 + b3. And again: (a 3 + …

The binomial theorem formula is (a+b) n = ∑ nr=0n C r a n-r b r, where n is a positive integer and a, b are real numbers, and 0 < r ≤ n. This formula helps to expand the binomial expressions such as (x + …

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. …

The binomial theorem is a fundamental result in algebra that provides a formula for expanding expressions of the form (a + b)n, where "a" and "b" are any numbers or variables, and "n" is a non …

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!

Nov 30, 2025 · The theorem states that for any given positive integer n, the expansion of the binomial expression (a + b) n can be expressed as the sum of n + 1 terms, where each term is a coefficient …

Learn about the Binomial Theorem Formula, and how you can use it to carry out Binomial Theorem Expansion in the A-Maths Syllabus.

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.

The binomial theorem states a formula for expressing the powers of sums. The most succinct version of this formula is shown immediately below. Isaac Newton wrote a generalized form of the Binomial …