Find the number to add to x^2+8x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.
To find the number to add to x^2 + 8x to make it a perfect square trinomial, we take half of the coefficient of the x term (8) and square it.
Half of 8 is 4, and 4 squared is 16.
Therefore, we need to add 16 to x^2 + 8x to make it a perfect square trinomial.
The trinomial as the square of a binomial is:
(x + 4)^2 = x^2 + 8x + 16