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AS Mathematics

This guide aims to build confidence in using brackets and factorizing linear expressions in algebra. It covers essential techniques such as expanding brackets using term-by-term multiplication and collecting like terms. You'll learn about methods like the grid method and the difference of squares formula. Additionally, it introduces common factors and the highest common factor (HCF) through practical examples. Enhance your algebra skills with these strategies to simplify expressions effectively and verify your answers through re-expansion.

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AS Mathematics

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  1. AS Mathematics Algebra – Manipulation of brackets

  2. Objectives • Be confident in the use of brackets • Be able to factorise linear expressions

  3. Review of expanding brackets multiply term by term collect like terms

  4. Alternatives for expanding (x + 3)(x + 5) grid method smiley face x2 +5x +3x +15

  5. Perfect square! Remember (a + b)2 = a2 + 2ab + b2

  6. Difference of 2 squares! Remember (a-b)(a+b)= a2 - b2

  7. – A harder one! multiply term by term collect like terms

  8. Example 5 multiply any two brackets multiply remaining bracket collect like terms

  9. Factorising This involves taking out any common factors. Try to spot the HCF by inspection.

  10. (i) common factors The HCF of 12x & 18y is 6 Check your answer by expanding the brackets The HCF of 6x2 & 21x is 3x

  11. (ii) grouping The first two terms have common factor a, the last two have common factor y There is now a common factor of (x + y) Check your answer by expanding the brackets.

  12. To illustrate this:- let z = x + y but z = x + y …..as before!

  13. The first two terms have common factor x, the last two have common factor 3 There is now a common factor of (y + 2) Check your answer by expanding the brackets.

  14. For this method to succeed, both brackets should be the same, i.e both (1 - y) Check your answer by expanding the brackets

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