Factorisation

Factorisation

1. The opposite of expanding

2. Process

   • Step 1- Check for common factors
   • Step 2- Count the number of terms
     • If there are 2 terms check for DOPS OR grouping 2 & 2
     • If there are 3 terms check for perfect square OR trinomial

3. Always check your answer for a common factor OR like terms OR DOPS

4. Common Factors

   • If there are already brackets in the question, expand the brackets and then factorise
     • 6(x-1)+2 = 6x-6+2 = 6x-4 = 2(3x-2)
   • Placed outside the bracket
     • 2x-4y= 2(x-2y)

5. DOPS

   • Difference of Perfect Squares OR Difference of Two Squares (DOTS)
   • Looks like a^2 * b^2
   • Always check for a common factor first
     • 2x^2 -50 = 2(x^2 -25) = 2(x^2 -5^2) = 2(x-5)(x+5)
   • Example
     • x^2-4 = x^2 - 2^2 = (x-2)(x+2)

6. Grouping 2 & 2

   • When you have 4 terms with no obvious common factor, sometimes it is easier to group the ones with common facotors
     • Once grouped, take out the common factor from each of the brackets
       • Try to have the same thing inside both brackets
         • Place the thing inside the brackets in it's bracket out the front. Place what is left in the second bracket
   • Example
     • 3y^2 - 2xy - 6y +4x = y(3y-2x) -2 (3y-2x) = (3y-2x)(y-2)