Factorisation

Factorisation

The opposite of expanding
Process
1. Step 1- Check for common factors
2. Step 2- Count the number of terms
  1. If there are 2 terms check for DOPS OR grouping 2 & 2
  2. If there are 3 terms check for perfect square OR trinomial
Always check your answer for a common factor OR like terms OR DOPS
Common Factors
1. If there are already brackets in the question, expand the brackets and then factorise
  1. 6(x-1)+2 = 6x-6+2 = 6x-4 = 2(3x-2)
2. Placed outside the bracket
  1. 2x-4y= 2(x-2y)
DOPS
1. Difference of Perfect Squares OR Difference of Two Squares (DOTS)
2. Looks like a^2 * b^2
3. Always check for a common factor first
  1. 2x^2 -50 = 2(x^2 -25) = 2(x^2 -5^2) = 2(x-5)(x+5)
4. Example
  1. x^2-4 = x^2 - 2^2 = (x-2)(x+2)
Grouping 2 & 2
1. When you have 4 terms with no obvious common factor, sometimes it is easier to group the ones with common facotors
  1. Once grouped, take out the common factor from each of the brackets
    1. Try to have the same thing inside both brackets
      1. Place the thing inside the brackets in it's bracket out the front. Place what is left in the second bracket
2. Example
  1. 3y^2 - 2xy - 6y +4x = y(3y-2x) -2 (3y-2x) = (3y-2x)(y-2)

Zusammenfassung der Ressource

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