document.write( "Question 818532: I'm doing my homework and I'm not sure with some of my answers. Can you help me? Here it is:
\n" ); document.write( " Find the product of [(d+e)-9]^2
\n" ); document.write( " Is that equal to d^2 + 2de + e^2 + 49 ? \n" ); document.write( "
Algebra.Com's Answer #492609 by jsmallt9(3759)\"\" \"About 
You can put this solution on YOUR website!
Short answer: No

\n" ); document.write( "\"%28%28d%2Be%29-9%29%5E2++\"
\n" ); document.write( "There are a couple of ways to figure this out:
  • Multiply it out:
    1. Rewrite as \"%28%28d%2Be%29-9%29%28%28d%2Be%29-9%29\"
    2. Multiply each term of the first (d+e)-9 times each term of the second (d+e)-9. This will be 9 multiplications!
    3. Add like terms, if any.
  • Use patterns:
    • \"%28a%2Bb%29%5E2=+a%5E2%2B2ab%2Bb%5E2\"
    • \"%28a-b%29%5E2=+a%5E2-2ab%2Bb%5E2\"
    • I am going to show you how to use the patterns.

    \n" ); document.write( "At first you might think: The patterns are for squaring two-term expressions but I'm trying to square a three-term expression. How is that possible?

    \n" ); document.write( "Well, the problem already has the d+e grouped. We can treat it as the \"a\" in \"%28a-b%29%5E2\". Using (d+e) as the \"a\" and the \"9\" as the \"b\", the pattern shows us how to square your expression:
    \n" ); document.write( "\"%28d%2Be%29%5E2-2%28d%2Be%29%289%29%2B%289%29%5E2++\"
    \n" ); document.write( "If you can't see the pattern in this, then check out the P.S. at the end. Simplifying the last parts:
    \n" ); document.write( "\"%28d%2Be%29%5E2-18%28d%2Be%29%2B81+\"
    \n" ); document.write( "\"%28d%2Be%29%5E2-18d-18e%2B81+\"
    \n" ); document.write( "To simplify the beginning we can use the \"%28a%2Bb%29%5E2\" pattern (in a more obvious way than above):
    \n" ); document.write( "\"%28d%29%5E2%2B2%28d%29%28e%29%2B%28e%29%5E2-18d-18e%2B81+\"
    \n" ); document.write( "which simplifies:
    \n" ); document.write( "\"d%5E2%2B2de%2Be%5E2-18d-18e%2B81+\"
    \n" ); document.write( "There are no like terms. So the expression is fully simplified.

    \n" ); document.write( "P.S. If you're having trouble with how we used the \"%28a-b%29%5E2\" pattern on \"%28%28d%2Be%29-9%29%5E2++\" then using a temporary variable can help:
    \n" ); document.write( "Let q = (d+e). Substituting this in for (d+e) we get:
    \n" ); document.write( "\"%28q-9%29%5E2++\"
    \n" ); document.write( "Use of the \"%28a-b%29%5E2\" pattern should be clear now:
    \n" ); document.write( "\"%28q%29%5E2-2%28q%29%289%29%2B%289%29%5E2\"
    \n" ); document.write( "which simplifies:
    \n" ); document.write( "\"q%5E2-18q%2B81\"
    \n" ); document.write( "Now we need to replace the \"q\" with \"(d+e)\":
    \n" ); document.write( "\"%28d%2Be%29%5E2-18%28d%2Be%29%2B81\"
    \n" ); document.write( "which is the same as we had earlier. It simplifies to the same answer we got above: \"d%5E2%2B2de%2Be%5E2-18d-18e%2B81+\"

    \n" ); document.write( "P.P.S. If you insist on multiplying \"%28%28d%2Be%29-9%29%5E2\" out instead of using the patterns, you should end up with the same result.     \n" ); document.write( "
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