49n2-84n+36

To verify if the expression 49n^2 - 84n + 36 is a perfect square of the form (an + b)^2, where a and b are integers, you can expand the square and see if it matches the given expression.

The square of (an + b) can be expanded using the formula (a^2n^2 + 2abn + b^2). Comparing this with the given expression:

49n^2 - 84n + 36

We can observe that the coefficient of the n^2 term is 49, so a^2 must be 49, which implies a = 7. Similarly, the constant term is 36, so b^2 must be 36, which implies b = 6.

Now let's expand (7n + 6)^2:

(7n + 6)^2 = (7n)^2 + 2(7n)(6) + (6)^2
= 49n^2 + 84n + 36

As you can see, the expanded form is exactly the same as the given expression. Therefore, it is correct to say that 49n^2 - 84n + 36 is a perfect square of 7n - 6.