Double Brackets (SQA National 5 Maths): Revision Note

Expanding double brackets

How do I expand double brackets?

• By double brackets we mean an expression such as

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

• You can do this by changing the double brackets into a pair of single brackets

  • Then use the usual method for expanding single brackets

• Split the terms in the first bracket, and multiply the second bracket by each of them separately

  • 

• Then expand and simplify the single brackets

  • 

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How do I expand double brackets using FOIL?

• Expanding 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 double brackets using a grid?

• You may prefer a more visual method using a grid

• To expand , 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 when there are multiple variables?

• All the same rules and methods apply as when there is just one variable

• Remember to only simplify like terms

• For example:

  • Expanding:

  • The terms can be combined

  • 

Expanding squared brackets

How do I expand a bracket squared?

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

• To expand (x + 3)²

  • Write it as (x + 3)(x + 3)

  • Then use one of the methods above

    • E.g. with FOIL: (x + 3)(x + 3) = x² + 3x + 3x + 9

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