Solution
Given the expression below
Let the number be k

To make it a perfect square, we apply the perfect square formula

Equating both equations

Equating the terms

Where the term added k is

Substituting for k into the expression

Hence, the trinomial is

The number to be added is 64
Writing the trinomial as the square of a binomial becomes

Hence, the square of the binomial is

Thus, the number to be added is 64 and the square of the binomial is (x - 8)²