Expanding Double Brackets (Cambridge (CIE) IGCSE Maths)

Expanding Two Brackets

How do I expand two brackets using FOIL?

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

  • Expanding (x  + 1)(x  + 3) requires 4 multiplications in total

• A good way to remember all the multiplications is FOIL

  • F = First: multiply together the first terms in each bracket

  • O = Outside: multiply the first term in the first bracket by the last term in the last bracket

    • Visually, these are the outer terms

  • I = Inside: multiply the last term in the first bracket by the first term in the last bracket

    • Visually, these are the inner terms

  • L = Last: multiply together the last terms in each bracket

• It helps to put negative terms in brackets when multiplying

• Simplify the final answer by collecting like terms (if there are any)

How do I expand two brackets using a grid?

• You may prefer a more visual method using a grid

• To expand (x  + 1)(x  + 3), write out the brackets as row and column headings of a grid

  • They can be in either direction

  • Remember to write the appropriate sign in front of each term

  	x	+1
  x
  +3

• For each cell in the grid, multiply the term in the row heading by the term in the column heading

  	x	+1
  x	x2	x
  +3	3x	3

• Add together all the terms inside the grid to get the answer

  • x²  + x  + 3x  + 3

• Collect like terms

• x²  + 4x  + 3

How do I expand a bracket squared?

• Remember that a square number is a number multiplied by itself

• Write (x  + 3)² as (x  + 3)(x  + 3) and use one of the methods above

  • With FOIL: (x  + 3)(x  + 3) = x²  + 3x  + 3x  + 9

  • Then collect like terms: x² + 6x + 9

• Do not make the common mistake of saying (x + 3)² is x²  + 3²

  • This cannot be true, try substituting in x = 1

    • you would get (1 + 3)² = 4² = 16 on the left

    • but 1² + 3² = 1 + 9 = 10 on the right