b) \( \frac{1}{5}(a+2 b)(5 a-10 b) \)

Let's dive into a cool simplification of the expression \( \frac{1}{5}(a+2 b)(5 a-10 b) \)! First, we can distribute the elements inside the parentheses. When we multiply \( (a + 2b)(5a - 10b) \), we will apply the distributive property, leading us to \( 5a^2 - 10ab + 10ab - 20b^2 \). Notice how the middle terms \( -10ab \) and \( +10ab \) cancel each other out, leaving us with \( 5a^2 - 20b^2 \). Now, when you multiply that simplified expression by \( \frac{1}{5} \), you'll ultimately find that it reduces down to \( a^2 - 4b^2 \) after factoring out a common term. It’s a beautifully neat polynomial that is a difference of squares!