SOLUTION: I'm doing my homework and I'm not sure with some of my answers. Can you help me? Here it is: Find the product of [(d+e)-9]^2 Is that equal to d^2 + 2de + e^2 + 49 ?

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Question 818532: I'm doing my homework and I'm not sure with some of my answers. Can you help me? Here it is:
Find the product of [(d+e)-9]^2
Is that equal to d^2 + 2de + e^2 + 49 ?
Found 2 solutions by jhunjiro, jsmallt9:
Answer by jhunjiro(67)   (Show Source): You can put this solution on YOUR website!

Solution:
[(d+e)-9]^2
(d+e)^2 -18(d+e)+81
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(d^2 +2de +e^2)-18d -18e +81
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d^2 +e^2 +2de -18d -18e +81
Final Answer: d^2 +e^2 +2de -18d -18e +81
Answer by jsmallt9(3759)   (Show Source): You can put this solution on YOUR website!
Short answer: No


There are a couple of ways to figure this out:
  • Use patterns:
    • I am going to show you how to use the patterns.

    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?

    Well, the problem already has the d+e grouped. We can treat it as the "a" in . Using (d+e) as the "a" and the "9" as the "b", the pattern shows us how to square your expression:

    If you can't see the pattern in this, then check out the P.S. at the end. Simplifying the last parts:


    To simplify the beginning we can use the pattern (in a more obvious way than above):

    which simplifies:

    There are no like terms. So the expression is fully simplified.

    P.S. If you're having trouble with how we used the pattern on then using a temporary variable can help:
    Let q = (d+e). Substituting this in for (d+e) we get:

    Use of the pattern should be clear now:

    which simplifies:

    Now we need to replace the "q" with "(d+e)":

    which is the same as we had earlier. It simplifies to the same answer we got above:

    P.P.S. If you insist on multiplying out instead of using the patterns, you should end up with the same result.