Expanding-Double-Brackets Wjec-Eduqas 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

  • <img alt=”12 x squared minus 10 x y minus 12 y squared” data-mathml=”<math ><semantics><mrow><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mi>x</mi><mi>y</mi><mo>-</mo><mn>12</mn><msup><mi>y</mi><mn>2</mn></msup></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”23″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2223%22%20width%3D%22142%22%20wrs%3Abaseline%3D%2217%22%3E%3C!–MathML%3A%20%3Cmath%20xml