Mathematics & Statistic Tutor Perth - SPSS Help   

To begin our journey, lets start with an example of multiplying brackets together and see the pattern.  Hopefully this will help us understand how to factorise a quadratic.

        (x  +  4)( x  +  5)

 I like to have a routine to follow so I always multiply my brackets out the same way.

1. Multiply the first term in the first bracket by all the terms in the second bracket.
    
2. Multiply the second term in the first bracket by all the terms in the second bracket.
    
3. Add/subtract all  these terms. Watch out for those minus signs!
    
4. Continue until the last term in the first bracket.

 (x  +  4)( x  +  5)

1. Multiply the first term in the first bracket by all the terms in the second bracket.
   (x  +  4)( x  +  5) = (x  x   x)  +  (x   x  5)
    there is more to come, this is just step one!
2. Multiply the second term in the first bracket by all the terms in the second bracket.
   (x  +  4)( x  +  5) =  (x   x   x)  +  (x   x  5)  + (4   x   x) +   (4  x  5) 
3. Stop as the first bracket only has two terms.  Notice we add or subtract all of these terms as appropriate.
4. (x  +  4)( x  +  5) =  x²    +  5 x   + 4 x  +  4  x 5
                                     =   x²    +  9 x    +   20