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New · Foundation CIE Core slides + packs · Angles, Area, Averages, Algebra, Equations, Graphs, Polygons, Ratio, Similar Shapes, Simultaneous Eqns, Speed & Travel, Data graphsNew · LS Topic videos (IMProject) · Similar Shapes, Speed & Travel, Ratio, Polygons, Averages, Area, Straight-line Graphs, Angles, Graphs of Data, Simultaneous Eqns, Solving Equations, Basic Algebra, PythagorasFoundation packs · YouTube lesson slots linked on matching CIE Core slides (3 Nov 2026)Worked exam catalogue · 384 videosCIE 291 · IB 44 · Pearson 49New walkthrough · CIE 0606/21 O/N Q12 — Velocity vectors; time of collisionVideo catalogue updated · 3 Nov 2026New · Foundation CIE Core slides + packs · Angles, Area, Averages, Algebra, Equations, Graphs, Polygons, Ratio, Similar Shapes, Simultaneous Eqns, Speed & Travel, Data graphsNew · LS Topic videos (IMProject) · Similar Shapes, Speed & Travel, Ratio, Polygons, Averages, Area, Straight-line Graphs, Angles, Graphs of Data, Simultaneous Eqns, Solving Equations, Basic Algebra, PythagorasFoundation packs · YouTube lesson slots linked on matching CIE Core slides (3 Nov 2026)Worked exam catalogue · 384 videosCIE 291 · IB 44 · Pearson 49New walkthrough · CIE 0606/21 O/N Q12 — Velocity vectors; time of collisionVideo catalogue updated · 3 Nov 2026

Topic summary · IGCSE handout

Basic Algebra summary

Basic algebra is about collecting like terms, expanding brackets carefully, and simplifying expressions before solving.

Open Learning Sheet — Basic AlgebraDownload Basic Algebra answers PDF

Files: 5_basic_algebra_handout.pdf · 5_basic_algebra_handout_answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

  • Like terms share the same letter powers: 3x+5x=8x3x+5x=8x, but 3x+5x23x+5x^2 cannot combine.
  • Expand: a(b+c)=ab+aca(b+c)=ab+ac; watch double negatives.
  • Substitute values only after simplifying when the question allows.

Worked example 1 — Collect like terms

Simplify 3a+5a−2a3a+5a-2a.

Working

6a6a

Add/subtract coefficients.

Worked example 2 — Expand and simplify

Expand 3(x−2)+43(x-2)+4.

Working

3x−23x-2

Distribute, then collect.

Worked example 3 — Factorise

Factorise 6x+96x+9.

Working

3(2x+3)3(2x+3)

Take out the HCF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning SheetAnswers PDF
WorksheetsTopic summariesTopic videos
Basic Algebra summary — worksheet & answers PDF