Sure, let's solve it step by step.
First, remember that a trinomial is a perfect square if it can be expressed in the form (ax+b)² or (ax-b)², which expands to ax²±2abx+b².
(i) x² + 14x + 49
Comparing it with (ax + b)², if we take '7' as the value of 'b', it forms a perfect square, which can be written as (x+7)².
(ii) a² - 10a + 25
Comparing it with (ax - b)², where '5' is the value of 'b', it forms a perfect square, which can be written as (a-5)².
(iii) 4x² + 4x + 1
Factoring 4 from the first two terms, gives us 4(x² + x) + 1. However, no value of 'b' would satisfy the equation to form (2x + b)².
(iv) 9b² + 12b + 16
Factoring 9 from the first two terms, gives us 9(b² + (4/3)b) + 16. However, no value of 'b' would satisfy the equation to form (3b + b)².
(v) 16x² - 16xy + y²
Comparing it with (ax - by)², where '4x' is the value of 'a' and 'y' is 'b', it forms a perfect square, which can be written as (4x - y)².
(vi) x² - 4x + 16
Comparing it with (ax - b)², if we take '2' as the value of 'b', it doesn't satisfy the equation because the last term is not the square of 'b'. Hence, it does not form a perfect square.
So, none of the given trinomials are perfect squares.