document.write( "Question 1209739: Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:\r
\n" ); document.write( "\n" ); document.write( "2mn - 18m + 5n - mn + 20m + 4n + ___ \n" ); document.write( "
Algebra.Com's Answer #850049 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Here's how to find the constant:\r
\n" ); document.write( "\n" ); document.write( "1. **Combine Like Terms:**
\n" ); document.write( " First, combine the like terms in the expression:\r
\n" ); document.write( "\n" ); document.write( " 2mn - 18m + 5n - mn + 20m + 4n + C = mn + 2m + 9n + C\r
\n" ); document.write( "\n" ); document.write( "2. **Factoring Pattern:**
\n" ); document.write( " We want this expression to be factorable into the form (m + a)(n + b) for some constants *a* and *b*. Expanding this factored form gives us:\r
\n" ); document.write( "\n" ); document.write( " mn + bm + an + ab\r
\n" ); document.write( "\n" ); document.write( "3. **Match Coefficients:**
\n" ); document.write( " Compare the coefficients of the terms in our simplified expression (mn + 2m + 9n + C) with the coefficients in the expanded factored form (mn + bm + an + ab):\r
\n" ); document.write( "\n" ); document.write( " * The coefficient of mn is 1 in both.
\n" ); document.write( " * The coefficient of m is 2, so b = 2.
\n" ); document.write( " * The coefficient of n is 9, so a = 9.
\n" ); document.write( " * The constant term is C, and it must equal ab.\r
\n" ); document.write( "\n" ); document.write( "4. **Solve for C:**
\n" ); document.write( " Since a = 9 and b = 2, we have:\r
\n" ); document.write( "\n" ); document.write( " C = ab = (9)(2) = 18\r
\n" ); document.write( "\n" ); document.write( "Therefore, the constant is 18. The factored expression is (m+9)(n+2).
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