To transform the expression x² + 16x into a perfect square trinomial, we need to identify the appropriate value to add.
A perfect square trinomial is expressed in the form (a + b)², which expands to a² + 2ab + b². Here, a is x, and 2ab represents the linear term. In our case, we have:
- a = x
- 2ab = 16x
From 2ab = 16x, we can divide both sides by 2:
- ab = 8x
This means:
- b = 8
Now, to find the value to add, we need to calculate b²:
- b² = 8² = 64
Thus, the expression x² + 16x can be transformed into a perfect square trinomial by adding 64. Therefore, the complete expression becomes:
- x² + 16x + 64 = (x + 8)²
In conclusion, the value that must be added to the expression x² + 16x to make it a perfect square trinomial is 64.