Factorising quadratic equations

My question is why did the teacher factorise it like this and how did he make the decision to do it like this. Read the problem below. {for this problem * is squared as i cant do little 2s!!} Problem: 36x* - 4 My sons answer: (6x + 2)(6x -2) His teachers answer: 4(3x + 1)(3x - 1) We can see that the teachers answer is correct and much neater that ours but how did he decide to take this 4 out of the brackets can anyone explain the thought process behind this so we can apply it to future problems.
Question asked by: vicjam

Asked on: 21 Sep 2009

When you have this:
(6x + 2)(6x -2)

Then you can clearly see that all the numbers are a common multiple of 2. This gives us the opportunity to take that outside of the brackets and reduce it, in the same that we can reduce the fraction 6/2 = 3/1 = 3

So, dividing through by two gives us:
(3x + 1)(3x - 1)

Now, since we have divided both brackets by 2, then we need to multiply the brackets by 2 x 2 to preserve the solution, which is 4, and thus in total we get:

4(3x + 1)(3x - 1)

To check understanding, how would you reduce this:

(6x + 3)(6x - 3)

... see if you get the right answer (to check if you do, after the reduction multiply out and see both give the same answer).
By: knowitall
Replied at: 27 Sep 2009
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