Quandaries and Queries
Who is asking: Student
Any shortcuts are appreciated. I'm usually pretty good in math, but I just can't grasp this, I just don't get it.
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 = 53 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
To be more formal. Let y = x2 then
Factor this expression then replace y by x2 and see if the resulting expression can be further factored.