How many ordered pairs of positive real numbers (a, b) satisfy the equation

$$(1+2 a)(2+2 b)(2 a+b)=32 a b?$$

**Answer Choices**

A. 0

B. 1

C. 2

D. 3

E. an infinite number

How many ordered pairs of positive real numbers (a, b) satisfy the equation

$$(1+2 a)(2+2 b)(2 a+b)=32 a b?$$

**Answer Choices**

A. 0

B. 1

C. 2

D. 3

E. an infinite number