Distributive Property Calculator
Enter the outside factor and the two terms inside the brackets to expand using the distributive property.
The distributive property says a(b + c) = a·b + a·c: the factor outside the brackets multiplies every term inside. For a(bx + c) it gives (a·b)x + (a·c). This is how you remove brackets, and it is the reverse of factoring out a common factor.
How to Use This Calculator
Enter the factor sitting outside the brackets, then the coefficient of the variable term and the constant inside the brackets. You can change the variable letter if your expression uses something other than x. The calculator multiplies the outside factor through both inside terms and shows the expanded expression.
This is the standard first step in simplifying or solving many algebraic expressions, where brackets have to be removed before like terms can be combined.
How the Calculation Works
The distributive property states that multiplying a sum is the same as multiplying each part of the sum and adding the results. So the outside factor is multiplied by the variable term and, separately, by the constant term.
Signs matter: multiplying by a negative factor flips the sign of every term inside, which is where most mistakes happen. The calculator carries the signs through for you.
a(bx + c) = (a·b)x + (a·c)
Worked Example
Expand 3(2x + 4). Multiply the 3 by each term: 3 × 2x = 6x and 3 × 4 = 12. So 3(2x + 4) = 6x + 12.
With a negative factor, −3(2x + 4) = −6x − 12, because the −3 changes the sign of both terms inside the brackets.
Assumptions and Limitations
- Expands a single factor over a two-term bracket, a(bx + c)
- Handles negative and decimal coefficients
- Does not combine with other terms outside the brackets
- For factoring (the reverse), find the greatest common factor instead
When to Use a Distributive Property Calculator
Pre-algebra and algebra students use this to expand expressions like a(bx + c) using the distributive property, step by step. It is a reliable homework check and a way to learn the pattern of multiplying through parentheses. Enter the expression to see it expanded and simplified.
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Open calculator →Frequently Asked Questions
What is the distributive property?
It states that a(b + c) = ab + ac — a factor outside brackets multiplies every term inside. It lets you remove brackets by distributing the multiplication across the sum.
How do you distribute a negative number?
Multiply each term inside the brackets by the negative, flipping every sign. For example, −3(2x + 4) becomes −6x − 12, since the negative changes the sign of both terms.
Is distributing the opposite of factoring?
Yes. Distributing removes brackets by multiplying through; factoring adds brackets by pulling out a common factor. Each undoes the other, which is a useful check on your work.
Does the distributive property work with subtraction?
Yes. a(b − c) = ab − ac. Subtraction inside the brackets is just adding a negative, so the factor still multiplies each term and keeps the sign.
Can I distribute over three terms?
Yes. The property extends to any number of terms: a(b + c + d) = ab + ac + ad. This tool handles the common two-term case, a variable term plus a constant.
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