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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

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