Question 102539: is the following trinomial a perfect square?
x^2+18x+81
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Yes, it is a perfect square
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Since the coefficient (multiplier) of the x^2 term is 1, the first term can only be factored
to x times x. This means the two factors of x^2 + 18x + 81 must be of the form:
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(x + ____)*(x + ____)
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The blanks must be a factor pair of 81. The only pairs of factors of 81 are 81*1 and 9*9.
If you fill the blanks of the factors ... for checking ... with the pair of 9's you get:
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(x + 9)*(x + 9)
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If you multiply these out you will get x^2 + 18x + 81.
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But note that (x + 9)*(x + 9) = (x + 9)^2
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So the trinomial is equal to (x + 9)^2 and is, therefore, a perfect square.
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Hope this helps you to understand the problem.
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