Factorising / Factoring formulas

[Gringo123]

I had to factorise this formula. The answer that I came up with is below:

6ax - 12ay - 18a squared.

6(ax - 2ay - 3a squared)

My book says that the correct answer is:

6a(x - 2y - 3a)

Would my answer have been marked wrong in an exam? Why is the book's answer preferable to mine? What's the rule?

 

[danago]

Your answer is still mathematically valid, however in these types of problems it is generally expected that you use the biggest factor possible (biggest meaning the highest numeral possible, and all possible pronumerals). You correctly noted that 6 was a factor of each term, but you could have taken it a step further and noted that 6a was a factor also.

In my personal experience with exams and tests, your teacher would probably not give you full marks for your answer, as these types of problems are usually set to test your ability to factorize to the fullest extent.

 

[Gringo123]

Thank you once again for your help Danago!