Quandaries and Queries
Who is asking: Student
The essential of factoring is recognizing a pattern. Three of the main patterns you need to recognize are
To be able to apply these facts you need to be able to look at an algebraic expression and see
For example in your first problem
there is a common factor of 3 so it can be written
Now I see a difference of cubes since 8 is 23 and hence
Now factor as a difference of cubes.
Problem 2 is similar. Take out a common factor and you will have a sum of cubes since x6 = (x2)3
Problem 4 is similar.
In problem 3, 16xy - 4x = 4x(4y - 1) so
In this expression 4y - 1 is almost a common factor. If the expression were
then 4y - 1 would be a common factor. Do you have a typo?