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Question 95765: I am having difficulty with this problem could you please help?
Factor each polynomial completely. To begin, state which method should be applied as the first step, given the guidelines of this section. Then continue the exercise and factor each polynomial completely.
m^4 - 9n^4
I am not sure if I start with GCF or trial and error, when I use these methods I am not sure the solving is correct either. Could you please help me to understand this problem? Thank you.
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! m^4 - 9n^4 [This is a perfect square. Think about what terms were taken twice (squared) to get each term?]
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Step #1: Factor each term:
m^4=m^2*m^2
9=3*3
n^4=n^2*n^2
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Step #2: You need to use trial-and-error to arrange the terms that equal the product of m^4-9n^4.
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(m^2-3n^2)(m^2-3n^2) [use the FOIL method to multiply and you will see that this arrangement doesn't work]
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(m^2+3n^2)(m^2+3n^2) [use the FOIL method to multiply and you will see that this arrangement doesn't work]
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(m^2-3n^2)(m^2+3n^2) [use the FOIL method to multiply and you will see that this arrangement WORKS]
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Also, you may want to memorize the "special products" in you book becasue you will see these products over and over again. The product above is a special product called the "difference of two squares" because you are subtracting two terms that are squared m^2 subtracted from (9n^2). Practice alot of these types of problems until you learn the special patterns so that when you see these again, you will automatically know the answer.
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