document.write( "Question 106574: Fully factor the following:\r
\n" ); document.write( "\n" ); document.write( "4a^2-(3a+1)^2\r
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\n" ); document.write( "\n" ); document.write( "I believe that I need to use decomposition to answer this, but I can't understand how to approach it. \n" ); document.write( "

Algebra.Com's Answer #77558 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Fully factor:
\n" ); document.write( " $\"4a%5E2-%283a%2B1%29%5E2\"$ Do you recognise this as the difference of two squares?
\n" ); document.write( "The difference of two squares is factorable as follows:
\n" ); document.write( " $\"A%5E2-B%5E2+=+%28A-B%29%28A%2BB%29\"$ In your problem, A = 2a while B = (3a+1), so...
\n" ); document.write( " $\"4a%5E2-%283a%2B1%29%5E2+=+%282a-%283a%2B1%29%29%282a%2B%283a%2B1%29%29\"$ Now simplfy this to get:
\n" ); document.write( " $\"%28-a-1%29%285a%2B1%29\"$
\n" ); document.write( "You can check this solution by multiplying these two factors to see if you get back the original expression. Let's try it using FOIL.
\n" ); document.write( " $\"%28-a-1%29%285a%2B1%29+=+-5a%5E2%2B6a%2B1\"$ = $\"4a%5E2-%289a%5E2%2B6a%2B1%29+=+4a%5E2-%283a%2B1%29%5E2\"$ \n" ); document.write( "

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