Expand Brackets Calculator

Expanding means multiplying out brackets to write an expression as a sum of terms, such as (2x + 3)(x − 4) = 2x² − 5x − 12. This calculator multiplies every term by every term, collects like terms with exact coefficients, and checks the result by comparing the original and expanded forms at several values of x.

Try:

How to use the expand brackets calculator

  1. Type the expression with brackets, using x.
  2. Press Calculate.
  3. Read the expanded form and the method.

Formula

(a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd
(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2

Worked example: (2x + 3)(x − 4)

  • Expression: (2x + 3)(x - 4)

✓ Answer checked

(2x+3) (x−4)=2x2−5x−12\left(2x + 3\right)\,\left(x - 4\right) = 2x^{2} - 5x - 12
Degree
2
Step-by-step working (2 steps)

  1. Multiply every term by every term Distributive law

    Each term in one bracket multiplies each term in the other (FOIL for two binomials).

    (2x+3) (x−4)\left(2x + 3\right)\,\left(x - 4\right)

  2. Collect like terms

    Add together terms with the same power of x.

    2x2−5x−122x^{2} - 5x - 12
Formulas used
(a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd
(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2
How this was checked
  • ✓ The original and expanded forms give the same value at five test points.

Frequently asked questions

How do I expand (2x + 3)(x − 4)?

Multiply each term by each term: 2x² − 8x + 3x − 12 = 2x² − 5x − 12.

What is (x + 1)³ expanded?

x³ + 3x² + 3x + 1.

What is FOIL?

First, Outer, Inner, Last: a way to remember the four products when expanding two binomials.

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