Learn to break algebraic expressions back into their multiplied factors, using common factors and identities in reverse.
The simplest factoring method is spotting a term common to every part of the expression, then pulling it out front, leaving the rest inside brackets.
Factorise: 6x + 9
3(2x + 3)
Factorise: 4a²b + 8ab²
4ab(a + 2b)
The identities you learned for expanding — (a+b)², (a−b)², and a²−b² — work in reverse too, letting you recognize and factor expressions that match those patterns.
Factorise: x² + 6x + 9
This matches (a+b)² with a=x, b=3: (x + 3)²
Factorise: y² − 16
This matches a² − b² with a=y, b=4: (y+4)(y−4)
1. Factorise: 10x + 15
2. Factorise: 6a²b − 9ab²
3. Factorise: x² + 8x + 16
4. Factorise: 9y² − 4
5. Factorise: a² − 10a + 25