Algebra · Algebraic manipulation
Chapter 1 · 3
The idea
Expanding brackets
Why a multiplier reaches every term inside a bracket, why double brackets need every-with-every (and where the middle term of a square comes from), and how three brackets fall to the same rule two at a time.
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In this lesson — start anywhere
Algebra · Algebraic manipulation
Expanding brackets
Why a multiplier reaches every term inside a bracket, why double brackets need every-with-every (and where the middle term of a square comes from), and how three brackets fall to the same rule two at a time.
Why it works
A bracket is a package
Expanding is the most-used move in all of algebra — solving, factorising, proof and calculus all lean on it, so a slip here echoes everywhere. The one idea: a bracket is a package; multiplying the package multiplies everything in it. means five copies of the whole of , so it must be — five copies of AND five copies of . Stopping halfway () means four of your five packages lost their . Picture a rectangle tall and wide: its area splits into a piece and a piece.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
Start freeTakes a minute — no card.