To find the missing term in the perfect square trinomial x² – 16x, we can use the formula for a perfect square trinomial, which is (a – b)² = a² – 2ab + b². In this case, we have:
- a² = x² (so a = x)
- -2ab = -16x (which means 2ab = 16x)
Now, substituting a with x, we have:
- 2x * b = 16
From here, we solve for b:
- b = 16/(2x) = 8
Now, we need to find b²:
- b² = 8² = 64
Thus, the missing term in the trinomial x² – 16x is 64. Therefore, the complete perfect square trinomial is:
- x² – 16x + 64 = (x – 8)²