Expand Brackets Calculator

Work out expand brackets instantly with clear inputs, formula shown and shareable results.

About Expand Brackets Calculator

Expanding two brackets multiplies every term in the first by every term in the second — the FOIL pattern. The x coefficient is the sum of the two cross products ad + bc.

Formula

Expanding

(ax + b)(cx + d) = acx² + (ad + bc)x + bd

Worked example

With the default values below, Expand Brackets Calculator returns Expanded form of 12x^2 + 7x - 10. Change any input above and every figure here is recalculated in your browser.

Inputs used

a in (ax + b)(cx + d): 3
b: -2
c: 4
d: 5

Results

Expanded form: 12x^2 + 7x - 10
Coefficient of x²: 12.000000
Coefficient of x: 7.000000
Constant term: -10.000000

Step by step

1Values used
2Expanding
3Expanded form= 12x^2 + 7x - 10
4Coefficient of x²= 12.000000
5Coefficient of x= 7.000000
6Constant term= -10.000000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Expand (3x − 2)(4x + 5).

12x² + 15x − 8x − 10 = 12x² + 7x − 10.

What does FOIL stand for?

First, Outer, Inner, Last — the four products you form, though the underlying rule is just the distributive law.