Algebra · Algebraic manipulation
Chapter 1 · 4
The idea
Factorising with common factors
Why factorising is expansion run backwards, what "factorise fully" demands, and why a difference of two squares splits instantly — plus what the factorised form is actually FOR.
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Algebra · Algebraic manipulation
Factorising with common factors
Why factorising is expansion run backwards, what "factorise fully" demands, and why a difference of two squares splits instantly — plus what the factorised form is actually FOR.
Why it works
Expanding, run backwards
Factorising turns up in nearly every algebra question the exam asks — solving, simplifying fractions, proof — because factorising is expanding in reverse: rewriting a sum as a product. : both terms are divisible by 3, so pull the 3 out front and record what's left inside: . Expanding the answer must recreate the original — that check is free and catches nearly every slip."Fully" means the HIGHEST common factor
"Factorise fully" means the HIGHEST common factor comes out — the biggest number that divides every coefficient, and each shared letter at its lowest power:Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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