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Maths Gcse Wjec-Eduqas Higher

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  1. Scatter-Graphs-And-Correlation Wjec-Eduqas Higher
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  2. Cumulative-Frequency-And-Box-Plots Wjec-Eduqas Higher
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  3. Histograms Wjec-Eduqas Higher
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  4. Statistical-Diagrams- Wjec-Eduqas Higher
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  5. Averages-Ranges-And-Data Wjec-Eduqas Higher
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  6. Combined-And-Conditional-Probability Wjec-Eduqas Higher
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  7. Tree-Diagrams- Wjec-Eduqas Higher
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  48. Completing-The-Square Wjec-Eduqas Higher
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  49. Factorising Wjec-Eduqas Higher
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  52. Introduction-To-Algebra Wjec-Eduqas Higher
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Exam code:C300

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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