Distributive Property Calculator
Enter numbers to see the distributive property in action: expand a(b + c) into ab + ac, or use FOIL to expand the product of two binomials (a + b)(c + d), with every step shown.
Mode
a × b + a × c
Write the expression
Distribute — multiply first term
Distribute — multiply second term
Add the products
- 1
First product a × b
3 × 4 = 12 - 2
Second product a × c
3 × 5 = 15 - 3
Sum ab + ac
12 + 15 = 27
How does this calculator work?
The distributive property says a(b+c) = ab + ac — multiply the outside factor by each term inside. For two binomials, FOIL gives (a+b)(c+d) = ac + ad + bc + bd. Enter real numbers (positive, negative or decimal) and every multiplication step is shown, ending with the total.
Formula
How this is calculated
The distributive property states that multiplication distributes over addition: a(b + c) = ab + ac. This means you can expand the product by multiplying the factor outside the parentheses by each term inside and then adding the results. The rule holds for any real numbers — positive, negative, fractions, or decimals — and is one of the fundamental axioms of arithmetic and algebra.
When both factors are sums — (a + b)(c + d) — each term in the first factor multiplies each term in the second, giving four products. The mnemonic FOIL describes the order: First (a·c), Outer (a·d), Inner (b·c), Last (b·d). Adding the four products gives the expanded form. For numeric inputs the result is a single number; in symbolic algebra the products would be collected into like terms.
The distributive property is the basis for polynomial multiplication, factoring, and many algebraic identities. A direct check confirms the result equals a × (b + c) or (a + b) × (c + d) computed straightforwardly, verifying no arithmetic errors.
Frequently asked questions
Yes. Negative values work fully — distributing a negative factor flips the sign of each term. For example, −3(4 + 5) = −12 + (−15) = −27.
FOIL stands for First, Outer, Inner, Last — an acronym for the four multiplications needed to expand (a + b)(c + d). It is simply the distributive property applied twice.
Yes. a(b − c) = ab − ac. You can treat it as a(b + (−c)) = ab + a(−c) = ab − ac. The same logic applies to binomial expansions with subtraction.
Also known as
TG we-Calculate Editorial Team. (2026). Distributive Property Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/distributive-property-old-calculator
TG we-Calculate Editorial Team. "Distributive Property Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/distributive-property-old-calculator.
TG we-Calculate Editorial Team, "Distributive Property Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/distributive-property-old-calculator
@misc{wecalculate_distributive_property_old_calculator, title = {Distributive Property Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/distributive-property-old-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?