Quadratic Expressions — Year 9 Revision Notes
These notes cover expanding the product of two brackets, expanding squares, and factorising quadratics of the form x² + bx + c — all at Year 9 (Stage 9) level.
Expanding two brackets
To expand (x + 2)(x + 3), multiply each term in the first bracket by each term in the second, then collect like terms: x² + 3x + 2x + 6 = x² + 5x + 6. A multiplication grid makes sure you include all four products.
Key Facts & Formulas
- (x + a)(x + b) = x² + (a + b)x + ab
- (x + 2)(x + 3) = x² + 5x + 6
Tips
- Multiply all four pairs of terms.
- Collect the two middle terms into one.
Expanding squares
A squared bracket means the bracket times itself: (x + 4)² = (x + 4)(x + 4) = x² + 8x + 16. Do not forget the middle term — squaring a bracket is not the same as squaring each term.
Key Facts & Formulas
- (x + a)² = x² + 2ax + a²
- (x + 4)² = x² + 8x + 16
Tips
- Write the bracket out twice before expanding.
- (x + a)² is never just x² + a².
Factorising quadratics
To factorise x² + bx + c, find two numbers that multiply to c and add to b. For x² + 7x + 12, the numbers 3 and 4 work, so it factorises to (x + 3)(x + 4). Watch the signs carefully when c or b is negative.
Key Facts & Formulas
- x² + bx + c = (x + p)(x + q), pq = c, p + q = b
- x² + 7x + 12 = (x + 3)(x + 4)
Tips
- List factor pairs of c, then check which adds to b.
- Check by expanding your brackets.
Revision Checklist
- I can expand the product of two brackets
- I can expand a squared bracket including the middle term
- I can factorise a quadratic of the form x² + bx + c
- I can check a factorisation by expanding
Frequently Asked Questions
Why is (x + 3)² not x² + 9?
Because squaring a bracket means multiplying it by itself: (x + 3)(x + 3). Expanding gives x² + 3x + 3x + 9 = x² + 6x + 9. The middle term 6x is lost if you just square each part.
Build strong foundations in Quadratic Expressions
A free trial class with Teacher Rig helps your Year 9 child master Quadratic Expressions now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Quadratic Expressions develops in IGCSE Algebra and Graphs (Cambridge 0580) →