SOLUTION: is the following trinomial a perfect square? x^2+18x+81

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
.
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:
.
(x + ____)*(x + ____)
.
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:
.
(x + 9)*(x + 9)
.
If you multiply these out you will get x^2 + 18x + 81.
.
But note that (x + 9)*(x + 9) = (x + 9)^2
.
So the trinomial is equal to (x + 9)^2 and is, therefore, a perfect square.
.
Hope this helps you to understand the problem.
.
RELATED QUESTIONS
Is the following trinomial a perfect square? Explain why or why not. x^2 � 18x + 81 (answered by rapaljer)

Is the following trinomial a perfect square? x^2 + 18x + 81 (answered by scott8148)

Is the following trinomial a perfect square? why or why not... (answered by josmiceli)

Is the following trinomial a perfect square? x2 + 18x +... (answered by Earlsdon)

Is the following trinomial a perfect square? x^2 + 18x + 81 I don't think it is.... (answered by Nate)

Find the constant term that should be added to make the following expression a... (answered by jim_thompson5910)

which value of C makes the expression x^2 + 18X +c perfect square trinomial.... (answered by Alan3354)

Choose the constant term that completes the perfect square trinomial. x� - 18x... (answered by lynnlo)

Could someone help me please. This is a trinomial not a polynomial. Find the constant... (answered by rapaljer)