SOLUTION: Is the following trinomial a perfect square? Explain why or why not. x^2 – 18x + 81

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Question 88265: Is the following trinomial a perfect square? Explain why or why not.
x^2 – 18x + 81


Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+18x+%2B+81
%28x-9%29%5E2

Yes! It is a perfect square trinomial essentially because the x^2 coefficient is 1, and if you take HALF of the middle term and SQUARE the result, you get the last term which is 81. In other words, if you take half of -18, you get -9, then if you square the (-9) you get 81, which is the last term of the trinomial. Therefore, it IS a perfect square trinomial!!

R^2