SOLUTION: Factor polynomial completely. To begin, state which method should be applied as the first step. Then continue and factor polynomial completely. m^4 – 9n^4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor polynomial completely. To begin, state which method should be applied as the first step. Then continue and factor polynomial completely. m^4 – 9n^4       Log On


   

Question 78159: Factor polynomial completely. To begin, state which method should be applied as the first step. Then continue and factor polynomial completely.
m^4 – 9n^4
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely:
m%5E4-9n%5E4 Do you see this binomial as the difference of two squares? %28m%5E2%29%5E2-%283n%5E2%29%5E2
The difference of two squares can be factored thus:
A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29 Applying this to the given binomial, you get:
m%5E4-9n%5E4+=+%28m%5E2%2B3n%5E2%29%28m%5E2-3n%5E2%29 Now you'll notice that the second parentheses contains the difference of two squares %28m%29%5E2-%28sqrt%283%29n%29%5E2which can be factored, as explained before:
m%5E2-3n%5E2+=+%28m%2Bsqrt%283%29n%29%28m-sqrt%283%29n%29
While the sum of two squares m%5E2%2B3n%5E2 can be factored, the factors do entail the use of complex numbers.
A%5E2%2BB%5E2+=+%28A%2BBi%29%28A-Bi%29
So, if you want to factor "completely", you would get:
where:i+=+sqrt%28-1%29