Concept · 4 steps · NESA MA4-ALG-C-01

The Distributive Law (expanding)

The one move that turns brackets into plain terms — and quietly does half your mental arithmetic too. Get it solid and factorising (its mirror image) comes for free.

1Where it comes fromIt's just the area of a rectangle, cut into two pieces. Watch a(b+c) = ab + ac fall out. 2How to do itMultiply the outside by every term inside — with a generator that throws pronumerals and negatives at you. 3Where it gets trickyForgetting the second term, and what a minus out the front does to the signs. 4Out in the wildFast head-multiplication, and running it backwards — the first step of factorising.

← This concept rests on

Multiplying Whole Numbers
Using Pronumerals
Adding and Subtracting Like Terms

→ It unlocks

Factorising Algebraic Expressions
Expanding Binomial Products
Solving Linear Equations