document.write( "Question 150727: How do you complelty factor out, x^2 + 12xy + 35y^2, whats the answer? \n" ); document.write( "

Algebra.Com's Answer #110651 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Here's what you're asking.
\n" ); document.write( " $\"x%5E2+%2B+12xy+%2B+35y%5E2=%28ax%2Bby%29%28cx%2Bdy%29\"$
\n" ); document.write( "When you multiply out the right hand side using the FOIL method you get,
\n" ); document.write( " $\"%28ax%2Bby%29%28cx%2Bdy%29=acx%5E2%2B%28ad%2Bbc%29xy%2Bbdy%5E2\"$
\n" ); document.write( "You know that
\n" ); document.write( "1. $\"ac=1\"$
\n" ); document.write( "2. $\"bd=35\"$
\n" ); document.write( "3. $\"ad%2Bbc=12\"$
\n" ); document.write( "Your choice of numbers has to satisfy all three equations.
\n" ); document.write( "Let's focus on 2 and factors of 35.
\n" ); document.write( "Let b=5, d=7.
\n" ); document.write( "then 3 becomes,
\n" ); document.write( "3. $\"5a%2B7c=12\"$
\n" ); document.write( "If we let a=c=1, we can satisfy both 1 and 3.
\n" ); document.write( " $\"x%5E2+%2B+12xy+%2B+35y%5E2=%28x%2B5y%29%28x%2B7y%29\"$
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