Distributive Property Calculator

What this calculator does

So, you want to work out an expression with brackets, like 2 times the quantity 3 plus 4, and see the result. This tool evaluates it. You type an arithmetic expression, including brackets and the usual operations, and it returns the value.

It is built around the distributive property, and you can use it to watch that property hold: an expression with a bracket gives the same answer whether you add first or distribute first.

How to use it

1. Type an expression, using * for multiply and brackets for grouping, such as 2*(3 + 4).
2. Press Calculate.

The distributive property

The distributive property is one of the basic laws of arithmetic. It says that multiplying a number by a sum is the same as multiplying by each part of the sum and then adding. In symbols, a times the quantity b plus c equals a times b plus a times c. So the multiplication is spread, or distributed, across the addition. It works with subtraction too: a times the quantity b minus c equals a times b minus a times c. This law is what lets you break a bracket open, and it is used constantly in algebra, from tidying expressions to multiplying polynomials.

Seeing it with numbers

The property is easiest to trust when you see it play out. Take 2 times the quantity 3 plus 4. One way is to add first: 3 plus 4 is 7, and 2 times 7 is 14. The other way is to distribute: 2 times 3 is 6, 2 times 4 is 8, and 6 plus 8 is 14. Both roads reach 14, which is exactly what the distributive property promises. Entering the bracketed form into this tool gives 14, and you can confirm the distributed version gives the same, making the abstract rule concrete.

How the tool evaluates your expression

Behind the scenes, the tool hands your typed expression to a mathematics library called math.js, which reads the expression, respects the order of operations and the brackets, and computes the result. This is why you can type a fairly free-form expression rather than filling in fixed boxes: the library parses whatever valid arithmetic you give it. It evaluates to a single number, so it shows you the value of the expression rather than rewriting it symbolically, which is all you need to check the distributive property against a worked-out answer.

A worked example

Enter 2*(3 + 4). The tool evaluates the bracket first, getting 7, then multiplies by 2 to return 14. To see the distributive property, enter 2*3 + 2*4 instead: it returns 14 again. The two expressions, one bracketed and one distributed, agree, which is the property in action.

Why the property matters

The distributive property is the engine behind a great deal of algebra. It is what you use to expand a bracket, to multiply a term across a polynomial, and, applied twice, to multiply two binomials, which is the FOIL method. It also works in reverse: spotting a common factor and pulling it outside a bracket is the distributive property run backwards, which is the basis of factoring. So this humble rule, that multiplication spreads over addition, sits underneath expanding, factoring, and multiplying expressions. The FOIL calculator shows the two-binomial case that builds directly on it.

Questions people ask

What is the distributive property?

The rule that a times the quantity b plus c equals a times b plus a times c. Multiplication spreads across the terms of a sum.

What does this tool return?

The numerical value of the expression you type, worked out with the order of operations and brackets respected.

How does it show the distributive property?

Enter a bracketed expression and its distributed form separately. They give the same value, confirming the property.

How do I type the expression?

Use * for multiplication and brackets for grouping, like 2*(3 + 4). The tool reads standard arithmetic.

How does this connect to FOIL?

FOIL is the distributive property applied twice, to multiply two binomials. The FOIL calculator handles that case.

References

On the distributive property. Multiplication distributes over addition, so a times the quantity b plus c equals a times b plus a times c.

1. "Distributive property," Wikipedia, on the law relating multiplication and addition, a(b + c) = ab + ac.
2. "A Brief History of Algebra with a Focus on the Distributive Law and Semiring Theory," arXiv, on the history of the distributive law from the ancient Greeks to Boole naming it in 1847.