expanding brackets calculator

Supports x, parentheses, +, -, *, /, and ^. Implicit multiplication works: 2x(x+1).

If you are practicing algebra, a fast way to check your work is to expand expressions and compare your answer immediately. This expanding brackets calculator takes a bracketed expression, multiplies everything correctly using the distributive law, and returns a simplified polynomial in descending powers of x.

What does “expanding brackets” mean?

Expanding brackets means rewriting products of expressions as a sum (or difference) of terms. In algebra, this is powered by the distributive property:

a(b + c) = ab + ac

For two binomials, you may know this as FOIL:

  • First: multiply first terms
  • Outer: multiply outer terms
  • Inner: multiply inner terms
  • Last: multiply last terms

Example: (x + 3)(x - 2) = x² + x - 6.

How to use this expanding brackets calculator

1) Enter your expression

Type any valid expression with brackets, such as:

  • (x+4)(x-7)
  • (2x-5)(3x+1)
  • (x+2)^2
  • 2x(x-3)(x+1)

2) Click “Expand Brackets”

The calculator tokenizes your input, handles implied multiplication, applies operator precedence, and computes the simplified polynomial.

3) Review the final result

You will see the standardized interpretation and the expanded form. This helps you catch formatting issues quickly.

Supported input rules

  • Variable supported: x (uppercase X also works).
  • Allowed operators: +, -, *, /, ^.
  • Parentheses are supported for grouping.
  • Implicit multiplication is supported, e.g., 3x(x+2).
  • Division is supported only by constants (for polynomial output), e.g., (2x+4)/2.
  • Exponents must be non-negative integers, e.g., (x+1)^4.

Common mistakes when expanding brackets

Missing a term in multiplication

Every term in one bracket must multiply every term in the other bracket. Skipping one product is one of the most common errors.

Sign errors

Negative signs are easy to drop. Always check - × - = + and - × + = -.

Not combining like terms

After expansion, collect terms with the same power of x. For example, 2x + 5x becomes 7x.

Practice examples

  • (x+5)(x+2) = x^2 + 7x + 10
  • (x-3)(x-4) = x^2 - 7x + 12
  • (2x+1)(x-6) = 2x^2 - 11x - 6
  • (x+1)^3 = x^3 + 3x^2 + 3x + 1

Why this helps in algebra

Bracket expansion appears in equation solving, factorization checks, calculus preparation, and polynomial modeling. Using a reliable calculator saves time and gives you immediate feedback, especially when expressions get longer.

Use it as a checker while practicing by hand: solve first, then verify here.

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