Expanding and factorising · Year 10
In Year 10 you learn: factorising quadratics.
Expanding removes brackets by multiplying every term inside by what is outside. Factorising does the opposite: it puts brackets back in by taking out common factors. Both are everyday tools for simplifying algebra and solving equations.
Key facts
- Expand a single bracket by multiplying every term inside: 3(2x − 5) = 6x − 15.
- Expand two brackets by multiplying each term in the first by each term in the second (FOIL or a grid): (x + 2)(x + 5) = x² + 7x + 10.
- (a + b)² = a² + 2ab + b² — not a² + b².
- Factorise fully by taking out the highest common factor of the numbers and letters: 6x² + 9x = 3x(2x + 3).
- To factorise x² + bx + c, find two numbers that multiply to c and add to b.
Worked examples
Example 1
Expand (x + 4)(x − 7).
Answer: x² − 3x − 28
Example 2
Factorise x² − x − 12.
Answer: (x − 4)(x + 3)
Example 3
Factorise 3x² + 10x − 8.
Answer: (3x − 2)(x + 4)