Distributive Property Calculator

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

Outer Factor (a):

First Term (b):

Second Term (c):

Step-by-Step Solution:

Understanding the Distributive Property

The distributive property is a fundamental rule in algebra that helps simplify expressions by multiplying a single term across a sum or difference inside parentheses. It states that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The Distributive Property Formula

The standard algebraic representation of this property is:

a(b + c) = ab + ac

How to Use This Calculator

Outer Factor (a): Enter the number that is outside the parentheses.
First Term (b): Enter the first number inside the parentheses.
Second Term (c): Enter the second number inside the parentheses.
Calculate: Click the button to see the expansion and final result.

Real-World Example

Imagine you are buying lunch for 4 people. Each person wants a sandwich for 8 units and a drink for 2 units. You can calculate the total in two ways:

Method 1: Sum first, then multiply: 4 * (8 + 2) = 4 * 10 = 40.
Method 2 (Distributive): Multiply each first, then sum: (4 * 8) + (4 * 2) = 32 + 8 = 40.

Both methods yield the same result, but the distributive property is essential when dealing with variables in algebra, such as 3(x + 5).

function calculateDistributive() { var a = parseFloat(document.getElementById('factorA').value); var b = parseFloat(document.getElementById('termB').value); var c = parseFloat(document.getElementById('termC').value); var resultDiv = document.getElementById('distributiveResult'); var step1 = document.getElementById('step1'); var step2 = document.getElementById('step2'); var finalAnswer = document.getElementById('finalAnswer'); if (isNaN(a) || isNaN(b) || isNaN(c)) { alert("Please enter valid numbers for all fields."); return; } // Calculation Logic var product1 = a * b; var product2 = a * c; var total = product1 + product2; // Formatting output var sign = (c >= 0) ? "+" : "-"; var absC = Math.abs(c); step1.innerHTML = "Step 1: Multiply " + a + " by each term: (" + a + " × " + b + ") + (" + a + " × " + c + ")"; step2.innerHTML = "Step 2: Solve the products: " + product1 + " + (" + product2 + ")"; finalAnswer.innerHTML = "Result: " + a + "(" + b + " + " + c + ") = " + total; resultDiv.style.display = 'block'; }