Question 95765
m^4 - 9n^4 [This is a perfect square.  Think about what terms were taken twice (squared) to get each term?]
.
Step #1:  Factor each term:
m^4=m^2*m^2
9=3*3
n^4=n^2*n^2
.
Step #2:  You need to use trial-and-error to arrange the terms that equal the product of m^4-9n^4.
.
(m^2-3n^2)(m^2-3n^2) [use the FOIL method to multiply and you will see that this arrangement doesn't work]
.
(m^2+3n^2)(m^2+3n^2) [use the FOIL method to multiply and you will see that this arrangement doesn't work]
.
(m^2-3n^2)(m^2+3n^2) [use the FOIL method to multiply and you will see that this arrangement WORKS]
.
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.
.