document.write( "Question 78159: Factor polynomial completely. To begin, state which method should be applied as the first step. Then continue and factor polynomial completely.
\n" ); document.write( "m^4 – 9n^4
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Algebra.Com's Answer #56055 by Earlsdon(6294) $\"\"$ $\"About$

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Factor completely:
\n" ); document.write( " $\"m%5E4-9n%5E4\"$ Do you see this binomial as the difference of two squares? $\"%28m%5E2%29%5E2-%283n%5E2%29%5E2\"$
\n" ); document.write( "The difference of two squares can be factored thus:
\n" ); document.write( " $\"A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29\"$ Applying this to the given binomial, you get:
\n" ); document.write( " $\"m%5E4-9n%5E4+=+%28m%5E2%2B3n%5E2%29%28m%5E2-3n%5E2%29\"$ Now you'll notice that the second parentheses contains the difference of two squares $\"%28m%29%5E2-%28sqrt%283%29n%29%5E2\"$ which can be factored, as explained before:
\n" ); document.write( " $\"m%5E2-3n%5E2+=+%28m%2Bsqrt%283%29n%29%28m-sqrt%283%29n%29\"$
\n" ); document.write( "While the sum of two squares $\"m%5E2%2B3n%5E2\"$ can be factored, the factors do entail the use of complex numbers.
\n" ); document.write( " $\"A%5E2%2BB%5E2+=+%28A%2BBi%29%28A-Bi%29\"$
\n" ); document.write( "So, if you want to factor \"completely\", you would get:
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where: $\"i+=+sqrt%28-1%29\"$
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