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Home > Subjects > Mathematics > Level 2 > 2.6 Algebra > Subject content > Expanding three brackets

  • Subject: Mathematics
  • AS: 91261
  • Level: 2
  • Credits: 4
  • External

Mathematics 2.6 Apply algebraic methods in solving problems

Expanding three brackets

Example

       (x + 5)(x + 2)(x – 3)

       = (x + 5)(x2 – 3x + 2x – 6)        Multiply out the second pair
                                                     of brackets

       = (x + 5)(x2 – x – 6)                 –3x + 2x = –x

       = x3 – x2 – 6x + 5x2 – 5x – 30   Multiply all terms in second
                                                      bracket by x and then everything
                                                      in second bracket by 5

       = x3 + 4x2 – 11x – 30               Add the x2 terms together:
                                                      – x2 + 5x2 = 4x2
                                                      and the x terms together:
                                                      – 6x – 5x = –11x

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