Question 636668
The term 16a^2 can be expessed as 4^2*a^2. Using the property that the product of two squares is equal to the square of the products, 16a^2 can be expressed as (4a)^2. Then the numerator is the difference of two perfect squares (4a)^2 and b^2, therefore can be factored into the product of the sum and difference  of the numbers being squared. In this case we have 
{(4a)^2 - b^2} = (4a + b)(4a - b)
You can check this factorization by "FOIL",
 (4a)*(4a) -4ab +4ab - b*b = (4a)^2 - b^2 =  16a^2 - b^2
Note that the "OI" terms of "FOIL" cancel. This does not happen when the two perfect squares are added.

Rewriting the given expression yields
  {(4a + b)(4a - b)}/(4a - b)
which simplifies to the quotient
   4a + b