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Algebra 1 Ch11.5 #11

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?
Thank You

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

(x-y) (x+y)

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.