Quandaries
and Queries 

Who is asking: Student Level: Secondary Question: Factor these: Any shortcuts are appreciated. I'm usually pretty good in math, but I just can't grasp this, I just don't get it. Thanks! 

Hi KJ, There are some patterns that you need to recognize to in order to factor. Three if these patterns are: the difference of squares
the difference of cubes
and the sum of cubes
For example, in your first problem, 125 = 5^{3} and thus this is a sum of cubes
In a similar way your second problem is a difference of cubes. Problem 3 doesn't match any of the three paterns above, in fact the exprerssion in problem 3 can't be factored. Problem 4 is again recognizing a pattern. When I look at problem 4 I see
where
To be more formal. Let y = x^{2} then
Factor this expression then replace y by x^{2} and see if the resulting expression can be further factored. Penny 

