Question from Josh:
I’m doing Jacob’s Elementary Algebra and I’m having difficulty on Lesson 11-5 problem 11. I don’t understand how to simplify the problem by looking for common factors. Would you be able to provide any help?
Answer from Dr. Callahan:
You have to take these in steps.
For a) you first look for something to simplify. You could multiply things out – but that would not help. Yet, if you look at the
x^2 – y^2 term you might remember (page 470) difference of two squares – which will help you remember that this is
which now will help you factor the rest
In b) you could take the 4x^2 + 2x and make it 2x(2x+1) which will help
in c) you can make the x^2-25 = (x+5)(x-5) like in a. You can also factor the x^2 – 10x +25 to get (x – 5)(x – 5)
in d) you can factor out the first numerator to get x (x^2+3) and then factor it out.
You just need to play with each term first and then see what cancels out. You might can do more that I have done here – but this should get you started.