Distributive Property Calculator – Guide & Formulas
Apply the distributive property to expand expressions. Calculate a(b + c) = ab + ac with step-by-step algebraic simplification and verification.
Apply the distributive property to expand algebraic expressions instantly. Enter values for a, b, and c to see a(b + c) broken into ab + ac with step-by-step work.
Key Takeaway
Use the free Distributive Property Calculator to apply the distributive property to expand expressions. calculate a(b + c) = ab + ac with step-by-step algebraic simplification and verification. Get instant results with step-by-step explanations.
How to Use the Distributive Property Calculator
- Enter the multiplier value (a) — the number outside the parentheses.
- Enter the first addend (b) — the first number inside the parentheses.
- Enter the second addend (c) — the second number inside the parentheses.
- Review the expanded form showing a × b + a × c with intermediate and final results.
The Formula
Variable Definitions
- a: The multiplier (the number outside the parentheses)
- b: The first addend inside the parentheses
- c: The second addend inside the parentheses
- ab: The product of a and b (first distributed term)
- ac: The product of a and c (second distributed term)
Expanding 5(3 + 7)
Apply the distributive property to expand 5(3 + 7).
- Step 1: Identify a = 5, b = 3, c = 7.
- Step 2: Distribute: 5(3 + 7) = 5 × 3 + 5 × 7.
- Step 3: Calculate first term: 5 × 3 = 15.
- Step 4: Calculate second term: 5 × 7 = 35.
- Step 5: Add the products: 15 + 35 = 50. Verify: 5(3 + 7) = 5 × 10 = 50. ✓
Frequently Asked Questions
What is the distributive property?
The distributive property states that a(b + c) = ab + ac. It means you can distribute the multiplication over addition (or subtraction) inside parentheses. It is one of the fundamental properties of arithmetic and algebra.
Does the distributive property work with subtraction?
Yes. a(b - c) = ab - ac. The same distribution applies, but the sign between the products follows the sign inside the parentheses. For example, 3(8 - 2) = 3×8 - 3×2 = 24 - 6 = 18.
Can I use the distributive property with variables?
Absolutely. The distributive property is essential in algebra: x(y + z) = xy + xz, and it works the same way with variables as with numbers. For example, 2(x + 3) = 2x + 6.
What is the reverse of the distributive property?
The reverse is called factoring. For example, ab + ac = a(b + c). Factoring extracts a common factor from terms, which is the opposite of expanding using the distributive property.
How does the distributive property apply to multi-term expressions?
When distributing over multiple terms, multiply the outside factor by each term inside: a(b + c + d) = ab + ac + ad. The same rule applies regardless of how many terms are inside the parentheses.
Is the distributive property the same as PEMDAS?
No, but they work together. PEMDAS (order of operations) tells you to evaluate parentheses first. The distributive property provides a way to simplify expressions by removing parentheses through distribution.
What is the distributive property of equality?
The distributive property of equality states that if a = b, then ac = bc. This means you can multiply both sides of an equation by the same number, which is fundamental for solving equations.
How is the distributive property used in mental math?
Use distribution to break difficult multiplications into easier parts. For example, 7 × 12 = 7(10 + 2) = 70 + 14 = 84. Or 25 × 16 = 25(10 + 6) = 250 + 150 = 400.