Double-Brackets Aqa Higher

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 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

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