Chapter 9: Algebraic expressions and expanding brackets

GCSE Skills

• You need to be able to work with algebraic expressions confidently
• You can use the index laws to simplify algebraic expressions
• You can square or cube a whole expression
  • Remember that if a letter appears on its own then it has the power 1
• Algebraic expressions may also contain negative and fractional indices

One at a time

• When you are multiplying expressions:
  • Multiply any number parts first
  • Add the powers of each letter to work out the new power
• When you are dividing expressions:
  • Divide any number parts first
  • Subtract the powers of each letter to work out the new power

Working it out

• Start by simplifying the top part of the fraction
• Do the number part first then the powers
• Next divide the expressions
• Divide the number part, then divide the indices

Expanding brackets

• Expanding or multiplying out brackets is a key algebra skill
• You have to multiply the expression outside the bracket by everything inside the bracket
• ‘Expand and simplify’ means multiply out and then collect like terms

Golden rule

• When you expand, you need to be careful with negative signs in front of the bracket
• Negative signs belong to the term to their right
  • Multiply out the brackets first and then collect like terms if possible

Methods

• You can use the grid method to expand two brackets
• Or you can use the acronym FOIL to expand two brackets
• Remembered as smiley face
  • First, outer, inner, last terms

Examiners report

• If you have to multiply three factors, don’t try to do it all in one step
• Expand and write brackets around the whole expansion
• Then multiply every terms inside the brackets by x