Quadratic Expressions
Expand the product of two brackets and factorise quadratic expressions of the form x² + bx + c.
Overview
Year 9 algebra steps up to quadratics. Students expand the product of two brackets, such as (x + 2)(x + 3), and reverse the process by factorising quadratic expressions of the form x² + bx + c. This is one of the most important skills for IGCSE, where quadratics appear in equations, graphs and problem solving.
What You Will Learn
- Expand the product of two binomials, e.g. (x + 2)(x + 3)
- Simplify the result by collecting like terms
- Expand squares such as (x + 4)²
- Factorise quadratic expressions of the form x² + bx + c
- Check a factorisation by expanding it again
Key Vocabulary
Common Mistakes to Avoid
- Forgetting the middle term when expanding, e.g. writing (x + 3)² as x² + 9
- Making sign errors when one or both terms are negative
- Choosing factors that multiply to c but do not add to b
- Only multiplying the first terms of each bracket
What Comes Next
At IGCSE this leads into solving quadratic equations by factorising, the quadratic formula, and quadratic graphs in the Algebra and Graphs topic.
Frequently Asked Questions
How do I expand two brackets?
Multiply every term in the first bracket by every term in the second, then collect like terms. For (x + 2)(x + 3): x×x + x×3 + 2×x + 2×3 = x² + 5x + 6. A grid or 'FOIL' helps you not miss a term.
How do I factorise x² + bx + c?
Find two numbers that multiply to c and add to b. For x² + 5x + 6, the numbers 2 and 3 multiply to 6 and add to 5, so it factorises to (x + 2)(x + 3).
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Algebra
- Framework ref
- 9Ae
- Difficulty
- High
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) →