To determine what number must be added to the expression x² + 8x to make it a perfect square trinomial, we can utilize the method of completing the square.
A perfect square trinomial takes the form (x + a)² = x² + 2ax + a². In our case, we can compare the given expression with this form.
The middle term, 8x, can be related to 2ax. Thus, we can find a by:
- Setting 2a = 8
- Solving for a: a = 8/2 = 4
Now that we have a = 4, we can find a²:
- a² = 4² = 16
This means that we need to add 16 to the original expression to complete the square.
Thus, the perfect square trinomial will be x² + 8x + 16 = (x + 4)².
So, the number that must be added is 16.