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Binomial Theorem Expansion Calculator

Expand (a + b)ⁿ up to n = 50 with exact coefficients, the Pascal triangle row, the general term and any single term you ask for — negative b handled sign by sign.

Related tools

All Algebra & equations tools →
Rational Root Theorem CalculatorEvery ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.Binomial Probability CalculatorGet P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.Negative Binomial Distribution CalculatorProbability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.Bayes Theorem CalculatorCompute the posterior probability P(A|B) with the probability tree, the natural-frequency restatement and the base-rate lesson that makes a 99 % accurate test right only 16.7 % of the time.Central Limit Theorem CalculatorProbabilities for a sample mean from the population mean, standard deviation and sample size, with the standard error and the z-scores shown.Pythagorean theorem calculatorFind any side of a right triangle — hypotenuse or leg — from the two you know, with the three squares drawn.Absolute Value Equation SolverSolve absolute-value equations like |x+3| = 5, 3|x+2| = 12 or |x+1| = |x−3| with step-by-step case analysis and exact solutions.Absolute Value Inequality SolverSolve absolute-value inequalities such as |x+3| < 5 or |x−2| > 3 and get the solution as an interval, with AND/OR reasoning explained step by step.

Binomial Theorem Expansion Calculator is free to use as often as you like, directly from this page. You will find it under Algebra & equations, with Rational Root Theorem Calculator and Binomial Probability Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Binomial Theorem Expansion Calculator do?

Expand (a + b)ⁿ up to n = 50 with exact coefficients, the Pascal triangle row, the general term and any single term you ask for — negative b handled sign by sign.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Binomial Theorem Expansion Calculator different from Rational Root Theorem Calculator?

They sit next to each other but answer different questions. Rational Root Theorem Calculator: every ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Binomial Probability Calculator is the closest one after this: Get P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.

What else is worth having open alongside it?

Negative Binomial Distribution Calculator and Bayes Theorem Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.ExplainerProbability Basics, With ExamplesProbability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.How-toHow to Calculate VolumeVolume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.How-toCircle: Circumference and AreaCircumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.