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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
    3 主题
  4. Statistical-Diagrams Aqa Higher
    5 主题
  5. Averages-Ranges-And-Data Aqa Higher
    7 主题
  6. Combined-And-Conditional-Probability Aqa Higher
    3 主题
  7. Tree-Diagrams Aqa Higher
    1 主题
  8. Simple-Probability-Diagrams Aqa Higher
    3 主题
  9. Transformations Aqa Higher
    5 主题
  10. Vectors Aqa Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
    4 主题
  13. Pythagoras-And-Trigonometry Aqa Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
    5 主题
  16. Volume-And-Surface-Area Aqa Higher
    3 主题
  17. Circles-Arcs-And-Sectors Aqa Higher
    2 主题
  18. Area-And-Perimeter Aqa Higher
    4 主题
  19. Circle-Theorems Aqa Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
    3 主题
  22. Symmetry-And-Shapes Aqa Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Aqa Higher
    2 主题
  24. Standard-And-Compound-Units Aqa Higher
    5 主题
  25. Direct-And-Inverse-Proportion Aqa Higher
    2 主题
  26. Problem-Solving-With-Ratios Aqa Higher
    2 主题
  27. Ratios Aqa Higher
    3 主题
  28. Sequences Aqa Higher
    4 主题
  29. Transformations-Of-Graphs Aqa Higher
    2 主题
  30. Graphing-Inequalities Aqa Higher
    2 主题
  31. Solving-Inequalities Aqa Higher
    2 主题
  32. Real-Life-Graphs Aqa Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
    2 主题
  34. Equation-Of-A-Circle Aqa Higher
    2 主题
  35. Functions Aqa Higher
    3 主题
  36. Forming-And-Solving-Equations Aqa Higher
    3 主题
  37. Graphs-Of-Functions Aqa Higher
    6 主题
  38. Linear-Graphs Aqa Higher
    4 主题
  39. Coordinate-Geometry Aqa Higher
    4 主题
  40. Iteration Aqa Higher
    1 主题
  41. Simultaneous-Equations Aqa Higher
    2 主题
  42. Quadratic-Equations Aqa Higher
    4 主题
  43. Linear-Equations Aqa Higher
    1 主题
  44. Algebraic-Proof Aqa Higher
    1 主题
  45. Rearranging-Formulas Aqa Higher
    2 主题
  46. Algebraic-Fractions Aqa Higher
    4 主题
  47. Completing-The-Square Aqa Higher
    1 主题
  48. Factorising Aqa Higher
    6 主题
  49. Expanding-Brackets Aqa Higher
    3 主题
  50. Algebraic-Roots-And-Indices Aqa Higher
    1 主题
  51. Using-A-Calculator Aqa Higher
    1 主题
  52. Surds Aqa Higher
    2 主题
  53. Rounding-Estimation-And-Bounds Aqa Higher
    2 主题
  54. Fractions-Decimals-And-Percentages Aqa Higher
    3 主题
  55. Introduction Aqa Higher
    7 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
    4 主题
  57. Percentages Aqa Higher
    3 主题
  58. Fractions Aqa Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Aqa Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
    4 主题
  61. Number-Operations Aqa Higher
    10 主题
课 Progress
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Exam code:8300

Expanding three brackets

How do I expand three brackets?

  • Multiply out any two of the brackets using a standard method and simplify

  • Then multiply the resulting expression by the third (unused) bracket

  • This step often looks like (x + a)(x2 + bx + c)

  • Every term in the first bracket must be multiplied with every term in the second bracket

  • A grid can help to keep track of all the terms

    • E.g. (x + 2)(x2 + 3x + 1)

      x2

      +3x

      +1

      x

      x3

      3x2

      x

      +2

      2x2

      6x

      2

  • Add all the terms inside the grid together

    • x3 + 2x2 + 3x2 + 6x + x + 2

  • Simplify by collecting any like terms

    • x3 + 5x2 + 7x + 2

Worked Example

Expand open parentheses 2 x minus 3 close parentheses open parentheses x plus 4 close parentheses open parentheses 3 x minus 1 close parentheses.

Expand and simplify the first two brackets, for example using the FOIL method

<img alt=”table row blank blank cell open parentheses 2 x minus 3 close parentheses open parentheses x plus 4 close parentheses end cell row blank equals cell 2 x cross times x plus 2 x cross times 4 plus open parentheses negative 3 close parentheses cross times x plus open parentheses negative 3 close parentheses cross times 4 end cell row blank equals cell 2 x squared plus 8 x minus 3 x minus 12 end cell row blank equals cell 2 x squared plus 5 x minus 12 end cell end table” data-mathml=”<math ><semantics><mtable columnspacing=”0px” columnalign=”right center left”><mtr><mtd/><mtd/><mtd><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></mtd></mtr><mtr><mtd/><mtd><mo>=</mo></mtd><mtd><mn>2</mn><mi>x</mi><mo>&#215;</mo><mi>x</mi><mo>+</mo><mn>2</mn><mi>x</mi><mo>&#215;</mo><mn>4</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mo>&#215;</mo><mi>x</mi><mo>+</mo><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mo>&#215;</mo><mn>4</mn></mtd></mtr><mtr><mtd/><mtd><mo>=</mo></mtd><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>12</mn></mtd></mtr><mtr><mtd/><mtd><mo>=</mo></mtd><mtd><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>12</mn></mtd></mtr></mtable><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab 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