Expanding Brackets & Factoring Algebraic Expressions Packet + Solutions

Master expanding brackets and factorising algebraic expressions with this comprehensive, print-and-go 14-page practice booklet. This resource features 7 carefully scaffolded sections covering everything from single/double brackets to perfect squares, common factors, difference of two squares, and quadratic trinomials, complete with full step-by-step worked solutions for easy marking or independent revision.

What’s Included in This 14-Page Resource?
• 8 Pages of High-Utility Worksheets: Cleanly formatted, print-and-go handouts ready to print and distribute to your class.
• 6 Pages of Full, Step-by-Step Worked Solutions Key: Every single problem is fully expanded showing the complete mathematical progression—ideal for quick teacher marking, student peer-assessment, or independent home study.

Scaffolding & Question Progression
• Section 1: Expand Single Brackets: Basic distribution with positive, negative, and fractional multipliers, such as 2(x + 3) or -5(3n + 1).
• Section 2: Expand & Simplify (Linear): Multi-term expressions requiring distribution followed by collecting like terms, such as 3(x + 1) + 8 or 5x - 4(2x - 1).
• Section 3: Advanced Linear Expansion: Distributing variables and expanding multiple bracket sets simultaneously, such as x(x + 2) + 3(x + 1).
• Section 4: Expand Double Brackets: FOIL or grid method practice for binomial distribution with varying sign combinations, such as (x + 2)(x + 3) or (3y - 2)(5y - 1).
• Section 5: Perfect Squares: Squaring binomial expressions using single and multiple variables, such as (x + 2)^2 or (2a - 5b)^2.
• Section 6: Factorise Fully (Common Factors): Pulling out the highest common monomial factor from linear and higher-degree terms, such as 5x + 10 or 4x^2 + 2x.
• Section 7: Advanced Factorising (Difference of Squares & Trinomials): Identifying structural patterns to factorise quadratic difference of two squares and trinomials where a=1 and a>1, such as 4x^2 - 9 or 2x^2 - x - 15.

Why Teachers and Cover Staff Love This Resource:
• Ready to Use: Simply print, staple, and hand out! Perfect for busy term schedules, multi-day units, or unexpected cover lessons.
• Extensive Step-by-Step Solutions: Saves you hours of marking time and allows students to self-assess or fix errors independently.
• Versatile Classroom Utility: Ideal for core secondary maths instruction, targeted revision, homework tasks, short assessments, or focused exam prep.

Target Audience, Exam Boards, & Specifications:
• Key Stages: Key Stage 3 (Extension) and Key Stage 4 (GCSE Foundation and Higher Tiers).
• Exam Board Alignment: Fully suitable for AQA, Edexcel, OCR, and iGCSE specifications requiring expanding and factorising expressions.
• Subject Areas: GCSE Mathematics, Secondary School Maths, and Core Maths.