Expanding & Factorising

Previous Section: Surds

Next Section: Quadratics

Word Doc (Exp. & Factorising Only)

Word Doc (Whole Chapter)

PDF (Expanding & Factorising Only)

PDF (Whole Chapter)

AS Maths – Pure – Expanding Brackets

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1B Slides (Courtesy of Owen134866)

Dr Frost Video

• 123 Expand a single bracket with an integer on the front. Key Skill Video (GCSE)
• 124 Expand two sets of single brackets and collect like terms. Key Skill Video (GCSE)
• 318 Expanding two brackets with simple coefficients. Key Skill Video (GCSE)
• 319 Expanding two brackets. Key Skill Video (GCSE)
• 320 Expanding three brackets. Key Skill Video (GCSE)

Bicen Maths Live Lesson

No Bicen Maths Live Lesson for This Section

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 7-9

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 252f: Expand a single bracket with each term involving multiple variables or constants, using index laws.
• 252m: Expand and simplify two sets of single brackets, where multipliers are variables or terms.
• 299e: Expand double brackets given in the form (x ± a)²
• 299f: Expand double brackets given in the form (ax ± b)(cx ± d)
• 299h: Expand double brackets given in the form (a ± bx)(c ± dx)
• 299j: Expand double brackets with up to three terms in a single bracket.
• 299k: Expand double brackets given in the form (ax ± b)(cx² ± dx ± e)
• 299l: Expand a single term and two brackets given in the form ax(bx ± c)(dx ± e)
• 299m: Expand double brackets involving index laws.
• 299p: Expand and simplify the sum of two double bracket expansions.
• 299q: Expand and simplify the difference of two double bracket expansions.
• 299r: Expand an expression given in the form (ax ± b)² – (cx± d)²
• 299s: Expand an expression given in the form (a±b/x)²
• 300a: Expand an expression given in the form (x ± a)(x ± b)(x ± c)
• 300b: Expand an expression given in the form (x ± a)(bx ± c)(dx ± e)
• 300c: Expand an expression given in the form (ax ± b)(cx ± d)(ex ± f)
• 300d: Expand an expression given in the form (ax ± b)³
• 300e: Expand an expression given in the form (ax+b)²(cx+d)
• 300f: Expand an expression given in the form (ax+b)³+(cx+d)²
• 252: Exam Practice: Expanding a single bracket
• 299: Exam Practice: Expanding double brackets
• 300: Exam Practice: Expanding three (or more) brackets

Other Videos

Expanding Single Brackets

Expanding Double Brackets

Expanding Triple Brackets

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• WW GCSE/IGCSE Expanding Brackets
• Berwick Maths Diagnostic Questions

Worksheets

• kutasoftware Worksheets
  • Multiplying a Polynomial and a Monomial
  • Multiplying Binomials
  • Multiplying Polynomials
  • Multiplying Special Case Polynomials
• MadAsMaths (T. Madas)
  • Identities Q1–2, 4, 6 (difficulty 2 of 5)
  • Polynomials Exam Questions (Intro) Q1, 6–7 (difficulty 2 of 5)
  • Polynomials Practice (Intro) Simplifying Expressions Q8–10
  • Basic Skills Q9–10 · questions only

AS Maths – Pure – Factorising

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1C Slides (Courtesy of Owen134866)

Dr Frost Video

• 170 Factorising by taking a common numeric factor out. Key Skill Video (GCSE)
• 171 Factorising by taking a common algebraic factor out. Key Skill Video (GCSE)
• 321 Factorising quadratics of the form x²+bx+c. Key Skill Video (GCSE)
• 322 Factorising quadratics of the form x²−bx+c. Key Skill Video (GCSE)
• 323 Factorising quadratics of the form x²±bx−c. Key Skill Video (GCSE)
• 324 Factorising quadratics of the form x²±bx±c. Key Skill Video (GCSE)
• 325 Factorise the difference of two squares. Key Skill Video (GCSE)
• 371 Factorising quadratics of the form ax²+bx+c. Key Skill Video (GCSE)

Bicen Maths Live Lesson

No Bicen Maths Live Lesson for this Section

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 10-14

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 253c: Factorise out a common algebraic factor involving index laws.
• 253d: Factorise out a common algebraic factor involving index laws for an expression with three or more terms.
• 253e: Expand an expression then factorise fully by taking out a single term.
• 362a: Factorise quadratic expressions given in the form x² +bx + c
• 362b: Factorise quadratic expressions given in the form x² – bx + c
• 362c: Factorise quadratic expressions given in the form x² +bx – c
• 362d: Factorise quadratic expressions given in the form x² – bx – c
• 363a: Factorise the difference of two squares given in the form x² – a² or a² – x²
• 363b: Factorise the difference of two squares given in the form kx²-a², where k is a square number.
• 363d: Factorise the difference of two squares given in the form ax²-by², where a and b have a common numeric factor.
• 364a: Factorise quadratic expressions given in the form ax² +bx+c with a>1
• 364b: Factorise quadratic expressions given in the form ax²-bx+c with a>1
• 364c: Factorise quadratic expressions given in the form ax² + bx – c with a>1
• 364d: Factorise quadratic expressions given in the form ax² -bx – c with a>1
• 364e: Factorise quadratic expressions given in the form ax² ± bx ± c where a>1 and a, b and c share a common factor.
• 364f: Factorise quadratic expressions requiring rearrangement to the form ax² ± bx ± c with a>1
• 365a: Factorise an expression with a common bracket, without powers.
• 365i: Factorise a cubic expression by first taking out a common factor.
• 365j: Factorise a cubic expression by grouping into pairs of terms.
• 365k: Factorise a quartic expression using the difference of two squares.
• 253: Exam Practice: Factorising out a single term
• 362: Exam Practice: Factorising quadratic expressions given in the form x² + bx + c
• 363: Exam Practice: Factorising the difference of two squares
• 364: Exam Practice: Factorising a quadratic where the coefficient of the x² term is not 1
• 365: Exam Practice: Factorising more difficult expressions by combining factorisation techniques or substitution of a variable

Other Videos

Factorising Single Brackets

Factorising Quadratics

Factorising Harder Quadratics

Factorising Harder Quadratics 2

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• WW GCSE/IGCSE Factorising
• Berwick Maths Diagnostic Questions

Worksheets

• kutasoftware Worksheets
  • Factoring Quadratic Polynomials (Easy, Hard)
  • Factoring Special Case Polynomials
  • Factoring by Grouping
• Mathshelper (Jon Stone)
  • Factorising Hard
• MadAsMaths (T. Madas)
  • Identities Q9, 15 (difficulty 3 of 5)
  • Quadratics Exam Questions Q24, 39, 52, 64, 85, 88 (difficulty 3–5 of 5)
  • Basic Skills Q17–26 · questions only

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Jethwa Maths Worksheet (p1-3)
• Naiker Maths Exam Qs (2005-2011)✦ & MS✦ (Whole Chapter)
• Naiker Maths Exam Qs (2012-2017) & MS (Whole Chapter)
• Crash Maths Whole Chapter Test✦ (Solutions Pending)
• SRWhitehouse Factorising Quadratics✦ (TES Account Required)
• PMT
  • Edexcel Set 2 Whole Chapter PPQs (Old Spec)
  • Further Questions at End of Polynomials Chapter
  • Summary Cheat Sheet
• Pret Homework (Rachel Mahoney)
  • Algebraic Manipulation (Rachel Mahoney, docx)

Worksheets

• Mathshelper (Jon Stone)
  • Algebra-Manipulation Further Practice
• Jethwa Maths
  • 10 Minute Starters: Algebraic expressions

Activities

• NRICH (student problems)
  • Algebra & Functions
• Andy Lutwyche
  • Erica's Errors On Algebraic Expressions