Expand Brackets Calculator
Multiply out brackets like (2a − b)² or 3(x + 2)(2x − 5), using the algebraic identities where they fit and showing every step.
About the Expand Brackets Calculator
Expanding means multiplying out the brackets and collecting like terms. Two brackets multiply term by term, which the area model shows as a grid. Common patterns have identities that save work: (a + b)², (a − b)², (a + b)(a − b) and (a + b)³.
Every step is proved exactly before it's shown: each new line is the same expression as the one before, for every value of the letters.
The formula
- (a − b)²
- a² − 2ab + b²
- (a + b)(a − b)
- a² − b²
- (x + a)(x + b)
- x² + (a + b)x + ab
- (a + b)³
- a³ + 3a²b + 3ab² + b³
Worked example
(2a − b)²
- a = 2a, b = −b in (a + b)² = a² + 2ab + b²
- = 4a² − 4ab + b²
Questions people ask
Is 2ab one variable or two?
Two: each letter is its own variable, so 2ab means 2 × a × b.
Can I use fractions?
Yes, like x/2 or 0.5y. The answer stays exact.
How do I go the other way?
Use the Factoring Calculator to turn an expanded expression back into brackets.