Final answer:
The value of 'b' in the expression to make it a perfect square is 56. Therefore, the expression 16x^2 + 56x + 49 can be factored as (4x + 7)^2.
Step-by-step explanation:
The expression in the question is a quadratic in the form of ax^2 + bx + c, and we are given the parts of the expression except for the value of 'b'. To factor this expression as a perfect square, it should take the form of (mx + n)^2, where m and n are real numbers. For an expression ax^2 + bx + c to be a perfect square, 'b' must be twice the product of the square roots of 'a' and 'c'.
Here, a = 16 (because of the term 16x^2), and c = 49 (because of the constant term 49). The square roots of a and c are 4 and 7, respectively. Thus, in this case, b must equal 2 * 4 * 7, which is 56. Therefore, the value of 'b' is 56, which means the expression can be factored as (4x + 7)^2.