document.write( "Question 515185: Find the LCM of (9+7r), (81-49r^2), and (9-7r)\r
\n" ); document.write( "\n" ); document.write( "Thanks,
\n" ); document.write( "Dee\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #343785 by drcole(72)\"\" \"About 
You can put this solution on YOUR website!
To find the least common multiple, we need to first factor each of the expressions. The first, \"9+%2B+7r\", and the third, \"9+-+7r\", cannot be factored, but the second, \"81+-+49r%5E2\", is the difference of two squares:\r
\n" ); document.write( "\n" ); document.write( "\"+81+=+9%5E2\" and \"49r%5E2+=+7%2A7%2Ar%2Ar+=+7%2Ar%2A7%2Ar+=+%287r%29%287r%29+=+%287r%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "Remembering that every difference of two squares \"a%5E2+-+b%5E2\" can be factored as:\r
\n" ); document.write( "\n" ); document.write( "\"a%5E2+-+b%5E2+=+%28a+%2B+b%29%28a+-+b%29\"\r
\n" ); document.write( "\n" ); document.write( "we get that\r
\n" ); document.write( "\n" ); document.write( "\"81+-+49r%5E2+=+%289+%2B+7r%29%289+-+7r%29\"\r
\n" ); document.write( "\n" ); document.write( "So we are trying to find the least common multiple of \"9+%2B+7r\", \"%289+%2B+7r%29%289+-+7r%29\", and \"9+-+7r\". The least common multiple of three expressions A, B, and C is the simplest expression that contains A, B, and C in its factorization. So the least common multiple has to contain at least one \"9+%2B+7r\" and one \"9+-+7r\" in its factorization, since those appear in A and C. Do we need anything else? No, because \"81+-+49r%5E2+=+%289+%2B+7r%29%289+-+7r%29\", so \"81+-+49r%5E2\" doesn't add any new factors to the least common multiple. So the least common multiple must be \"%289+%2B+7r%29%289+-+7r%29\" or \"81+-+49r%5E2\".
\n" ); document.write( "
\n" );