Distributive Property Calculator

Apply a(b + c) = ab + ac and verify both sides match.

a(b + c) 32
a·b 20
a·c 12

Formula: a(b + c) = ab + ac

Step-by-step with your numbers:
1. Values used:
2. a = 4
3. b = 5
4. c = 3
5.
6. a(b + c) = 32
7. a·b = a x b = 4 x 5 = 20
8. a·c = 12
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The distributive property lets you multiply a sum by multiplying each term separately.

How the Math Works

The Distributive Property Calculator applies the fundamental algebraic rule that multiplying a number by a sum yields the same result as multiplying the number by each addend separately and then adding those products. Specifically, for any real numbers a, b, and c, the equation a(b + c) = ab + ac holds true. This calculator takes your input values and demonstrates both sides of the equation, showing how the left side (the factored form) expands to match the right side (the distributed form).

Practical Applications

To use this calculator, simply enter the values for a, b, and c into their respective fields. The calculator will compute a(b + c) by first adding b and c, then multiplying by a. Simultaneously, it calculates ab + ac by multiplying a by each term individually before adding the results. This tool is invaluable for simplifying algebraic expressions, factoring polynomials, and solving equations where distribution is required.

Day-to-Day Use

Understanding the distributive property helps in everyday calculations involving percentages, shopping comparisons, and budget planning. For instance, when calculating a 15% discount on 3 items priced at $20 and 4 items at $30, you can quickly compute 0.15(3×20 + 4×30) or distribute to get 0.15×3×20 + 0.15×4×30. This mental math approach makes financial decisions faster and more accurate, whether you're comparing bulk discounts, calculating taxes, or splitting bills among friends.

Worked example

4(5 + 3) = 4·5 + 4·3 = 20 + 12 = 32.

FAQ

Does it work for subtraction?

Yes — a(b − c) = ab − ac.