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Distributive Property

Overview

The Rainbow Rule.

What is it?

Multiplying a value outside the parentheses to EVERY term inside the parentheses.

History

A fundamental axiom of real numbers, essential for polynomial multiplication.

Key Idea

Draw arrows (rainbows) from the outside number to each inside number.

Practice This Topic

Concept Guide

Plain English: Imagine you are a waiter. You have to give water to EVERYONE at the table (inside the parentheses), not just the first person. You 'distribute' the water.

Real-world example: Buying Combo Meals. If you buy 3 'Burger+Fry' combos, you have 3 Burgers AND 3 Fries. 3(B+F) = 3B + 3F.

How to do it

  1. Identify the number outside the ( ).
  2. Draw an arrow to the first term inside. Multiply.
  3. Draw an arrow to the second term inside. Multiply.
  4. Keep the sign (+/-) between them.
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Common Pitfall

Forgetting the second number. Students often write 2(x+3) as 2x + 3. Wrong! It must be 2x + 6.

Word Problem
"A ticket costs $10 and a drink costs $5. You buy 4 of each. Calculate using distribution."
Reasoning: 4(10 + 5). You can do 4(15) = 60. OR Distribute: 4(10) + 4(5) = 40 + 20 = 60.

Practice Examples

The Rainbow
2(x + 4) 2*x + 2*4 2x + 8
Multiply both parts.