1. ## Handling Factors

Hi there,
Could someone please give me some examples of factorising and go through them step by step (including factorising into 2 brackets, factor theroem and difference of 2 squares). I only have a few examples to work from and I'm finding it quite hard. Thank you.

2. Originally Posted by bobchiba
Hi there,
Could someone please give me some examples of factorising and go through them step by step (including factorising into 2 brackets, factor theroem and difference of 2 squares). I only have a few examples to work from and I'm finding it quite hard. Thank you.
For something like factoring a^2 - b^2 it is probably best simply to memorize them. Likely ones to come up are:
a^2 - b^2 = (a + b)(a - b)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
a^2 + 2ab + b^2 = (a + b)^2
a^2 - 2ab + b^2 = (a - b)^2

Then there are the ones that use the distributive property in reverse. These are always of the form:
ab + ac = a(b + c)

For example, consider 3x^3 - 27xy^2. What is common between the two of them? The factor 3x. So
3x^3 - 27xy = (3x)(x^2 - 9y^2)

But we aren't done yet! x^2 - 9y^2 = (x)^2 - (3y)^2 = (x + 3y)(x - 3y) so we have:
3x^3 - 27xy = (3x)(x^2 - 9y^2) = (3x)(x + 3y)(x - 3y)

I don't have time right now to go through factoring trinomials. Perhaps someone else will. If not I'll get back to you later.

-Dan