Answer:
To create a perfect-square binomial of the form (y - k)^2, we need to find the value of k such that:
the first term of the binomial is y^2 (which is already the case)
the second term of the binomial is -2ky (which corresponds to -36y in the given expression)
the third term of the binomial is k^2 (which corresponds to 81 in the given expression)
To find k, we can use the formula:
k = (1/2)*(-b/a)
where a is the coefficient of y^2, b is the coefficient of y, and we are looking for the value of k that makes the expression a perfect square.
In this case, a = 1 and b = -36, so:
k = (1/2)(-b/a) = (1/2)(-(-36)/1) = 18
Therefore, the missing number to create a perfect-square binomial is 18:
(y - 18)^2 = y^2 - 36y + 324