Lesson 4 — Distributive Property

Properties Review

Multiplication Properties
Identity	For any number a, a · 1 = a
Property of Zero	For any number a, a · 0 = 0
Inverse	For every number a/b, where a, b ≠ 0, there is exactly one number b/a such that (a/b) · (b/a) = 1.

Properties of Equality
Reflexive	For any numbers a, a = a
Symmetric	If a = b, then b = a
Transitive	If a = b and b = c, then a = c
Substitution	If a = b, then a may be replaced by b in any expression
Distributive	a(b + c) = ab + ac and a(b − c) = ab − ac
Commutative	a + b = b + a and ab = ba
Associative	(a + b) + c = a + (b + c) and (ab)c = a(bc)

What is the Distributive Property?

When a number (or variable) multiplies a group in parentheses, we can distribute it to each term inside.

a(b + c) = ab + ac
a(b − c) = ab − ac

Examples

3(x + 4) = 3x + 12
5(2y − 1) = 10y − 5
−2(n + 6) = −2n − 12

Why it works: think of an area model. If the length is a and the width is split into b and c, then the total area is the sum of two rectangles: ab + ac.

Distribute-It Sandbox

Choose values, then expand and simplify.

Outside

Inside 1

Inside 2

Visualize with an Area Model

We shade ab and ac as two rectangles. The total area equals the sum of the parts.

Sandbox Game — Match the Expansion!

Match a factored form to its expanded form.

Factored

Expanded

Score: 0 / 0

Try it — Expand or Factor

Question 1 of 5

More practice (unlocks as you answer correctly)

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