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Edexcel A Level Maths: Pure:復(fù)習(xí)筆記2.5.1 Expanding Brackets

Category: A-level課程, 國際課程, 教材筆記, 福利干貨 Date: 2022年10月25日 下午3:05

Expanding Brackets

What do I need to know about expanding brackets?

  • To expand brackets, the rule is that each term in one set of brackets must be multiplied by each term in the other set of brackets

2.5.1-Expanding-Brackets-Illustration

  • 'FOIL' is a special case of this, when each set of brackets contains two terms you can mulitply in order
    • e.g. to multiply out or expand these brackets (2x + 3)(x - 5)
      • First (2x?+ 3)(x?- 5) gives 2x2
      • Outside?(2x?+ 3)(x?- 5) gives -10x
      • Inside?(2x +?3)(x?- 5) gives +3x
      • Last?(2x?+ 3)(x?- 5)?gives -15
    • (2x + 3)(x - 5) =?2x2?-10x +3x -15 =?2x2?-7x -15
  • If you spot something like (a + b)2?or (a + b)3?just write the brackets out twice or three times respectively
    • e.g. (3x + 2)2?= (3x +2)(3x+2) = 9x2?+ 6x + 6x + 4 =?9x2?+ 12x + 4
  • If you are trying to expand something like?(a?+?b)n?for powers of?n?greater than 2 or 3, use the?binomial expansion
  • If you have to expand more than two sets of brackets, just expand them two at a time

Worked Example

2.5.1-Expanding-Brackets-Example

Worked Example

2.5.1-Expanding-Brackets-Multiple

 

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