How do I factor problems with multiple exponents and operations?

Question

Here are 2 examples of the problems I am struggling with:

 

16(11x-13)^2 - 25(2x+7)^2

 

(2x+3)^7(5x-1)^30(8x+1)^3 - (2x+3)^5(5x-1)^30(8x+1)^5

Answer 1

I will help you with the 2nd problem.  Note there is a common factor of

 

(2x+3)⁵(5x-1)³⁰(8x+1)³

 

Then

 

(2x+3)⁷(5x-1)³⁰(8x+1)³ - (2x+3)⁵(5x-1)³⁰(8x+1)⁵ = [(2x+3)⁵(5x-1)³⁰(8x+1)³][(2x+3)² - (8x+1)²]