Is the following trinomial a perfect square? x^2 + 18x + 81?

Question

Is the following trinomial a perfect square? x^2 + 18x + 81

Answer 1

yep
(x+9)^2

Answer 2

In order to solve this problem, factor out the quadratic trinomial you have specified:

x² + 18x + 81

To do this, split 18x into 9x + 9x:

x² + 18x + 81
= x² + 9x + 9x + 81

Next, factor x² + 9x by taking out an x:

x² + 9x + 9x + 81
= x(x + 9) + 9x + 81

Do the same for 9x + 81, but factor out a 9 instead of x:

x(x + 9) + 9x + 81
= x(x + 9) + 9(x + 9)

Because x and 9 are both multiplied by the same binomial, x + 9, you can use the distributive property which states that for real numbers a, b, and c:

ac + bc = (a + b)c
ab + cb = (a + c)b
ba + ca = (b + c)a

Using this property in the equation that has been obtained so far:

x(x + 9) + 9(x + 9)
= (x + 9)(x + 9)

Simplify this further:

(x + 9)(x + 9)
= (x + 9)²

Because your equation is the square of a binomial, x + 9, it is a perfect square.

Therefore, the answer is yes, x² + 18x + 81 is a perfect square trinomial.

Hope this helps!

Answer 3

yes it is.
A quick way to check for a perfect square is to make the coefficient of x^2 equal to 1 (which it already is). Next divide the coefficient of x by two and square it. If the answer is the constant then the trinomial is a perfect square. In this case 18/2 squared = 81.

Answer 4

x² + 18x + 81 = (x + 9)(x + 9) = (x + 9)²
Is a perfect square.

Answer 5

to know if the it is perfect square either get b^2 -4ac if it is 0 so it is perfect square
so 18^2 -4*81= 0

another way
if the cooficient of x^2 =1 so
f +/- b= 2sqr(c) so it is perfect square
get the square root of c i.e sqr(81) =9
9*2=18=b

Answer 6

Yes, it is.

(x + 9)^2

Answer 7

yes

(x+9)^2

Answer 8

it is

(x + 9)^2

perfect square

Answer 9

yes, you can factor it..
it is a perfect square...



it will become

(X+9)(X+9)=X^2 + 18 X + 81

X= -9
X=-9


easy question, eh...?